id	sid	tid	token	lemma	pos
ap-4182	1	1	acta	acta	PROPN
ap-4182	1	2	polytechnica	polytechnica	PROPN
ap-4182	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4182	1	4	/	/	SYM
ap-4182	1	5	ap.2017.57.0470	ap.2017.57.0470	PROPN
ap-4182	1	6	acta	acta	PROPN
ap-4182	1	7	polytechnica	polytechnica	PROPN
ap-4182	1	8	57(6):470–476	57(6):470–476	PROPN
ap-4182	1	9	,	,	PUNCT
ap-4182	1	10	2017	2017	NUM
ap-4182	1	11	©	©	PROPN
ap-4182	1	12	czech	czech	PROPN
ap-4182	1	13	technical	technical	PROPN
ap-4182	1	14	university	university	PROPN
ap-4182	1	15	in	in	ADP
ap-4182	1	16	prague	prague	PROPN
ap-4182	1	17	,	,	PUNCT
ap-4182	1	18	2017	2017	NUM
ap-4182	1	19	available	available	ADJ
ap-4182	1	20	online	online	ADV
ap-4182	1	21	at	at	ADP
ap-4182	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4182	1	23	numerical	numerical	ADJ
ap-4182	1	24	calculation	calculation	NOUN
ap-4182	1	25	of	of	ADP
ap-4182	1	26	the	the	DET
ap-4182	1	27	complex	complex	ADJ
ap-4182	1	28	berry	berry	NOUN
ap-4182	1	29	phase	phase	NOUN
ap-4182	1	30	in	in	ADP
ap-4182	1	31	non	non	ADJ
ap-4182	1	32	-	-	ADJ
ap-4182	1	33	hermitian	hermitian	ADJ
ap-4182	1	34	systems	systems	PROPN
ap-4182	1	35	marcel	marcel	PROPN
ap-4182	1	36	wagner∗	wagner∗	VERB
ap-4182	1	37	,	,	PUNCT
ap-4182	1	38	felix	felix	PROPN
ap-4182	1	39	dangel	dangel	PROPN
ap-4182	1	40	,	,	PUNCT
ap-4182	1	41	holger	holger	PROPN
ap-4182	1	42	cartarius	cartarius	PROPN
ap-4182	1	43	,	,	PUNCT
ap-4182	1	44	jörg	jörg	PROPN
ap-4182	1	45	main	main	ADJ
ap-4182	1	46	,	,	PUNCT
ap-4182	1	47	günter	günter	PROPN
ap-4182	1	48	wunner	wunner	PROPN
ap-4182	1	49	institut	institut	PROPN
ap-4182	1	50	für	für	PROPN
ap-4182	1	51	theoretische	theoretische	PROPN
ap-4182	1	52	physik	physik	PROPN
ap-4182	1	53	1	1	NUM
ap-4182	1	54	,	,	PUNCT
ap-4182	1	55	universität	universität	PROPN
ap-4182	1	56	stuttgart	stuttgart	PROPN
ap-4182	1	57	,	,	PUNCT
ap-4182	1	58	70550	70550	NUM
ap-4182	1	59	stuttgart	stuttgart	PROPN
ap-4182	1	60	,	,	PUNCT
ap-4182	1	61	germany	germany	PROPN
ap-4182	1	62	∗	∗	NOUN
ap-4182	1	63	corresponding	correspond	VERB
ap-4182	1	64	author	author	NOUN
ap-4182	1	65	:	:	PUNCT
ap-4182	1	66	marcel.wagner@itp1.uni-stuttgart.de	marcel.wagner@itp1.uni-stuttgart.de	NOUN
ap-4182	1	67	abstract	abstract	NOUN
ap-4182	1	68	.	.	PUNCT
ap-4182	2	1	we	we	PRON
ap-4182	2	2	numerically	numerically	ADV
ap-4182	2	3	investigate	investigate	VERB
ap-4182	2	4	topological	topological	ADJ
ap-4182	2	5	phases	phase	NOUN
ap-4182	2	6	of	of	ADP
ap-4182	2	7	periodic	periodic	ADJ
ap-4182	2	8	lattice	lattice	NOUN
ap-4182	2	9	systems	system	NOUN
ap-4182	2	10	in	in	ADP
ap-4182	2	11	tight	tight	ADV
ap-4182	2	12	-	-	PUNCT
ap-4182	2	13	binding	bind	VERB
ap-4182	2	14	description	description	NOUN
ap-4182	2	15	under	under	ADP
ap-4182	2	16	the	the	DET
ap-4182	2	17	influence	influence	NOUN
ap-4182	2	18	of	of	ADP
ap-4182	2	19	dissipation	dissipation	NOUN
ap-4182	2	20	.	.	PUNCT
ap-4182	3	1	the	the	DET
ap-4182	3	2	effects	effect	NOUN
ap-4182	3	3	of	of	ADP
ap-4182	3	4	dissipation	dissipation	NOUN
ap-4182	3	5	are	be	AUX
ap-4182	3	6	effectively	effectively	ADV
ap-4182	3	7	described	describe	VERB
ap-4182	3	8	by	by	ADP
ap-4182	3	9	pt	pt	X
ap-4182	3	10	-symmetric	-symmetric	ADJ
ap-4182	3	11	potentials	potential	NOUN
ap-4182	3	12	.	.	PUNCT
ap-4182	4	1	in	in	ADP
ap-4182	4	2	this	this	DET
ap-4182	4	3	framework	framework	NOUN
ap-4182	4	4	we	we	PRON
ap-4182	4	5	develop	develop	VERB
ap-4182	4	6	a	a	DET
ap-4182	4	7	general	general	ADJ
ap-4182	4	8	numerical	numerical	ADJ
ap-4182	4	9	gauge	gauge	NOUN
ap-4182	4	10	smoothing	smoothing	NOUN
ap-4182	4	11	procedure	procedure	NOUN
ap-4182	4	12	to	to	PART
ap-4182	4	13	calculate	calculate	VERB
ap-4182	4	14	complex	complex	ADJ
ap-4182	4	15	berry	berry	NOUN
ap-4182	4	16	phases	phase	NOUN
ap-4182	4	17	from	from	ADP
ap-4182	4	18	the	the	DET
ap-4182	4	19	biorthogonal	biorthogonal	ADJ
ap-4182	4	20	basis	basis	NOUN
ap-4182	4	21	of	of	ADP
ap-4182	4	22	the	the	DET
ap-4182	4	23	system	system	NOUN
ap-4182	4	24	’s	’s	PART
ap-4182	4	25	non	non	ADJ
ap-4182	4	26	-	-	ADJ
ap-4182	4	27	hermitian	hermitian	ADJ
ap-4182	4	28	hamiltonian	hamiltonian	NOUN
ap-4182	4	29	.	.	PUNCT
ap-4182	5	1	further	far	ADV
ap-4182	5	2	,	,	PUNCT
ap-4182	5	3	we	we	PRON
ap-4182	5	4	apply	apply	VERB
ap-4182	5	5	this	this	DET
ap-4182	5	6	method	method	NOUN
ap-4182	5	7	to	to	ADP
ap-4182	5	8	a	a	DET
ap-4182	5	9	one	one	NUM
ap-4182	5	10	-	-	PUNCT
ap-4182	5	11	dimensional	dimensional	ADJ
ap-4182	5	12	pt	pt	NOUN
ap-4182	5	13	-symmetric	-symmetric	ADJ
ap-4182	5	14	lattice	lattice	NOUN
ap-4182	5	15	system	system	NOUN
ap-4182	5	16	and	and	CCONJ
ap-4182	5	17	verify	verify	VERB
ap-4182	5	18	our	our	PRON
ap-4182	5	19	numerical	numerical	ADJ
ap-4182	5	20	results	result	NOUN
ap-4182	5	21	by	by	ADP
ap-4182	5	22	an	an	DET
ap-4182	5	23	analytical	analytical	ADJ
ap-4182	5	24	calculation	calculation	NOUN
ap-4182	5	25	.	.	PUNCT
ap-4182	6	1	keywords	keyword	NOUN
ap-4182	6	2	:	:	PUNCT
ap-4182	6	3	complex	complex	ADJ
ap-4182	6	4	berry	berry	NOUN
ap-4182	6	5	phase	phase	NOUN
ap-4182	6	6	;	;	PUNCT
ap-4182	6	7	pt	pt	X
ap-4182	6	8	symmetry	symmetry	NOUN
ap-4182	6	9	;	;	PUNCT
ap-4182	6	10	gauge	gauge	NOUN
ap-4182	6	11	smoothing	smoothing	NOUN
ap-4182	6	12	.	.	PUNCT
ap-4182	7	1	1	1	X
ap-4182	7	2	.	.	X
ap-4182	7	3	introduction	introduction	NOUN
ap-4182	7	4	due	due	ADP
ap-4182	7	5	to	to	ADP
ap-4182	7	6	their	their	PRON
ap-4182	7	7	robustness	robustness	NOUN
ap-4182	7	8	against	against	ADP
ap-4182	7	9	local	local	ADJ
ap-4182	7	10	defects	defect	NOUN
ap-4182	7	11	or	or	CCONJ
ap-4182	7	12	disorder	disorder	NOUN
ap-4182	7	13	topologically	topologically	ADV
ap-4182	7	14	protected	protect	VERB
ap-4182	7	15	states	state	NOUN
ap-4182	7	16	as	as	ADP
ap-4182	7	17	majorana	majorana	PROPN
ap-4182	7	18	fermions	fermions	PROPN
ap-4182	7	19	[	[	X
ap-4182	7	20	1–3	1–3	NOUN
ap-4182	7	21	]	]	X
ap-4182	7	22	are	be	AUX
ap-4182	7	23	of	of	ADP
ap-4182	7	24	high	high	ADJ
ap-4182	7	25	value	value	NOUN
ap-4182	7	26	for	for	ADP
ap-4182	7	27	physical	physical	ADJ
ap-4182	7	28	applications	application	NOUN
ap-4182	7	29	such	such	ADJ
ap-4182	7	30	as	as	ADP
ap-4182	7	31	quantum	quantum	ADJ
ap-4182	7	32	computation	computation	NOUN
ap-4182	7	33	[	[	X
ap-4182	7	34	4	4	NUM
ap-4182	7	35	]	]	PUNCT
ap-4182	7	36	.	.	PUNCT
ap-4182	8	1	however	however	ADV
ap-4182	8	2	,	,	PUNCT
ap-4182	8	3	no	no	DET
ap-4182	8	4	physical	physical	ADJ
ap-4182	8	5	system	system	NOUN
ap-4182	8	6	is	be	AUX
ap-4182	8	7	completely	completely	ADV
ap-4182	8	8	isolated	isolate	VERB
ap-4182	8	9	and	and	CCONJ
ap-4182	8	10	dissipation	dissipation	NOUN
ap-4182	8	11	can	can	AUX
ap-4182	8	12	have	have	VERB
ap-4182	8	13	an	an	DET
ap-4182	8	14	important	important	ADJ
ap-4182	8	15	influence	influence	NOUN
ap-4182	8	16	on	on	ADP
ap-4182	8	17	the	the	DET
ap-4182	8	18	states	state	NOUN
ap-4182	8	19	[	[	X
ap-4182	8	20	5	5	NUM
ap-4182	8	21	]	]	PUNCT
ap-4182	8	22	.	.	PUNCT
ap-4182	9	1	majorana	majorana	PROPN
ap-4182	9	2	fermions	fermion	NOUN
ap-4182	9	3	can	can	AUX
ap-4182	9	4	even	even	ADV
ap-4182	9	5	be	be	AUX
ap-4182	9	6	created	create	VERB
ap-4182	9	7	with	with	ADP
ap-4182	9	8	the	the	DET
ap-4182	9	9	help	help	NOUN
ap-4182	9	10	of	of	ADP
ap-4182	9	11	dissipative	dissipative	ADJ
ap-4182	9	12	effects	effect	NOUN
ap-4182	9	13	[	[	X
ap-4182	9	14	6	6	NUM
ap-4182	9	15	,	,	PUNCT
ap-4182	9	16	7	7	NUM
ap-4182	9	17	]	]	PUNCT
ap-4182	9	18	.	.	PUNCT
ap-4182	10	1	of	of	ADP
ap-4182	10	2	special	special	ADJ
ap-4182	10	3	importance	importance	NOUN
ap-4182	10	4	in	in	ADP
ap-4182	10	5	this	this	DET
ap-4182	10	6	context	context	NOUN
ap-4182	10	7	is	be	AUX
ap-4182	10	8	the	the	DET
ap-4182	10	9	case	case	NOUN
ap-4182	10	10	of	of	ADP
ap-4182	10	11	balanced	balanced	ADJ
ap-4182	10	12	gain	gain	NOUN
ap-4182	10	13	and	and	CCONJ
ap-4182	10	14	loss	loss	NOUN
ap-4182	10	15	as	as	SCONJ
ap-4182	10	16	described	describe	VERB
ap-4182	10	17	by	by	ADP
ap-4182	10	18	pt	pt	X
ap-4182	10	19	-symmetric	-symmetric	ADJ
ap-4182	10	20	complex	complex	NOUN
ap-4182	10	21	potentials	potential	VERB
ap-4182	10	22	[	[	X
ap-4182	10	23	8	8	NUM
ap-4182	10	24	]	]	PUNCT
ap-4182	10	25	,	,	PUNCT
ap-4182	10	26	which	which	PRON
ap-4182	10	27	has	have	AUX
ap-4182	10	28	attracted	attract	VERB
ap-4182	10	29	large	large	ADJ
ap-4182	10	30	interest	interest	NOUN
ap-4182	10	31	in	in	ADP
ap-4182	10	32	quantum	quantum	ADJ
ap-4182	10	33	mechanics	mechanic	NOUN
ap-4182	10	34	[	[	X
ap-4182	10	35	9–13	9–13	NOUN
ap-4182	10	36	]	]	PUNCT
ap-4182	10	37	.	.	PUNCT
ap-4182	11	1	the	the	DET
ap-4182	11	2	stationary	stationary	ADJ
ap-4182	11	3	schrödinger	schrödinger	ADJ
ap-4182	11	4	equation	equation	NOUN
ap-4182	11	5	was	be	AUX
ap-4182	11	6	solved	solve	VERB
ap-4182	11	7	for	for	ADP
ap-4182	11	8	scattering	scatter	VERB
ap-4182	11	9	solutions	solution	NOUN
ap-4182	11	10	[	[	X
ap-4182	11	11	14	14	NUM
ap-4182	11	12	]	]	PUNCT
ap-4182	11	13	and	and	CCONJ
ap-4182	11	14	bound	bind	VERB
ap-4182	11	15	states	state	NOUN
ap-4182	11	16	[	[	X
ap-4182	11	17	15	15	NUM
ap-4182	11	18	]	]	PUNCT
ap-4182	11	19	,	,	PUNCT
ap-4182	11	20	and	and	CCONJ
ap-4182	11	21	also	also	ADV
ap-4182	11	22	questions	question	NOUN
ap-4182	11	23	concerning	concern	VERB
ap-4182	11	24	other	other	ADJ
ap-4182	11	25	symmetries	symmetry	NOUN
ap-4182	11	26	[	[	X
ap-4182	11	27	16	16	NUM
ap-4182	11	28	,	,	PUNCT
ap-4182	11	29	17	17	NUM
ap-4182	11	30	]	]	PUNCT
ap-4182	11	31	as	as	ADV
ap-4182	11	32	well	well	ADV
ap-4182	11	33	as	as	ADP
ap-4182	11	34	the	the	DET
ap-4182	11	35	meaning	meaning	NOUN
ap-4182	11	36	of	of	ADP
ap-4182	11	37	non	non	ADJ
ap-4182	11	38	-	-	ADJ
ap-4182	11	39	hermitian	hermitian	ADJ
ap-4182	11	40	hamiltonians	hamiltonian	NOUN
ap-4182	11	41	have	have	AUX
ap-4182	11	42	been	be	AUX
ap-4182	11	43	discussed	discuss	VERB
ap-4182	11	44	[	[	X
ap-4182	11	45	18	18	NUM
ap-4182	11	46	,	,	PUNCT
ap-4182	11	47	19	19	NUM
ap-4182	11	48	]	]	PUNCT
ap-4182	11	49	.	.	PUNCT
ap-4182	12	1	their	their	PRON
ap-4182	12	2	influence	influence	NOUN
ap-4182	12	3	on	on	ADP
ap-4182	12	4	many	many	ADJ
ap-4182	12	5	-	-	PUNCT
ap-4182	12	6	particle	particle	NOUN
ap-4182	12	7	systems	system	NOUN
ap-4182	12	8	has	have	AUX
ap-4182	12	9	been	be	AUX
ap-4182	12	10	studied	study	VERB
ap-4182	12	11	mainly	mainly	ADV
ap-4182	12	12	in	in	ADP
ap-4182	12	13	the	the	DET
ap-4182	12	14	context	context	NOUN
ap-4182	12	15	of	of	ADP
ap-4182	12	16	bose	bose	NOUN
ap-4182	12	17	-	-	PUNCT
ap-4182	12	18	einstein	einstein	NOUN
ap-4182	12	19	condensates	condensate	NOUN
ap-4182	12	20	[	[	X
ap-4182	12	21	20–25	20–25	NUM
ap-4182	12	22	]	]	PUNCT
ap-4182	12	23	but	but	CCONJ
ap-4182	12	24	also	also	ADV
ap-4182	12	25	on	on	ADP
ap-4182	12	26	lattice	lattice	NOUN
ap-4182	12	27	systems	system	NOUN
ap-4182	12	28	[	[	X
ap-4182	12	29	26–31	26–31	PROPN
ap-4182	12	30	]	]	PUNCT
ap-4182	12	31	.	.	PUNCT
ap-4182	13	1	in	in	ADP
ap-4182	13	2	the	the	DET
ap-4182	13	3	latter	latter	ADJ
ap-4182	13	4	systems	system	NOUN
ap-4182	13	5	it	it	PRON
ap-4182	13	6	was	be	AUX
ap-4182	13	7	shown	show	VERB
ap-4182	13	8	that	that	SCONJ
ap-4182	13	9	pt	pt	NOUN
ap-4182	13	10	-symmetric	-symmetric	ADJ
ap-4182	13	11	complex	complex	ADJ
ap-4182	13	12	potentials	potential	NOUN
ap-4182	13	13	may	may	AUX
ap-4182	13	14	eliminate	eliminate	VERB
ap-4182	13	15	the	the	DET
ap-4182	13	16	topologically	topologically	ADV
ap-4182	13	17	protected	protect	VERB
ap-4182	13	18	states	state	NOUN
ap-4182	13	19	existing	exist	VERB
ap-4182	13	20	in	in	ADP
ap-4182	13	21	the	the	DET
ap-4182	13	22	same	same	ADJ
ap-4182	13	23	system	system	NOUN
ap-4182	13	24	under	under	ADP
ap-4182	13	25	complete	complete	ADJ
ap-4182	13	26	isolation	isolation	NOUN
ap-4182	13	27	[	[	X
ap-4182	13	28	26–30	26–30	NUM
ap-4182	13	29	,	,	PUNCT
ap-4182	13	30	32	32	NUM
ap-4182	13	31	,	,	PUNCT
ap-4182	13	32	33	33	NUM
ap-4182	13	33	]	]	PUNCT
ap-4182	13	34	.	.	PUNCT
ap-4182	14	1	however	however	ADV
ap-4182	14	2	,	,	PUNCT
ap-4182	14	3	in	in	ADP
ap-4182	14	4	some	some	DET
ap-4182	14	5	pt	pt	NOUN
ap-4182	14	6	-symmetric	-symmetric	ADJ
ap-4182	14	7	potential	potential	ADJ
ap-4182	14	8	landscapes	landscape	NOUN
ap-4182	14	9	they	they	PRON
ap-4182	14	10	can	can	AUX
ap-4182	14	11	survive	survive	VERB
ap-4182	14	12	[	[	X
ap-4182	14	13	28–32	28–32	NUM
ap-4182	14	14	,	,	PUNCT
ap-4182	14	15	34	34	NUM
ap-4182	14	16	]	]	PUNCT
ap-4182	14	17	,	,	PUNCT
ap-4182	14	18	which	which	PRON
ap-4182	14	19	has	have	AUX
ap-4182	14	20	been	be	AUX
ap-4182	14	21	confirmed	confirm	VERB
ap-4182	14	22	in	in	ADP
ap-4182	14	23	impressive	impressive	ADJ
ap-4182	14	24	experiments	experiment	NOUN
ap-4182	14	25	[	[	X
ap-4182	14	26	33	33	NUM
ap-4182	14	27	,	,	PUNCT
ap-4182	14	28	35	35	NUM
ap-4182	14	29	]	]	PUNCT
ap-4182	14	30	in	in	ADP
ap-4182	14	31	most	most	ADJ
ap-4182	14	32	theoretical	theoretical	ADJ
ap-4182	14	33	studies	study	NOUN
ap-4182	14	34	the	the	DET
ap-4182	14	35	topologically	topologically	ADV
ap-4182	14	36	protected	protect	VERB
ap-4182	14	37	states	state	NOUN
ap-4182	14	38	have	have	AUX
ap-4182	14	39	been	be	AUX
ap-4182	14	40	identified	identify	VERB
ap-4182	14	41	via	via	ADP
ap-4182	14	42	their	their	PRON
ap-4182	14	43	property	property	NOUN
ap-4182	14	44	to	to	PART
ap-4182	14	45	close	close	VERB
ap-4182	14	46	the	the	DET
ap-4182	14	47	energy	energy	NOUN
ap-4182	14	48	gap	gap	NOUN
ap-4182	14	49	of	of	ADP
ap-4182	14	50	the	the	DET
ap-4182	14	51	band	band	NOUN
ap-4182	14	52	structure	structure	NOUN
ap-4182	14	53	or	or	CCONJ
ap-4182	14	54	their	their	PRON
ap-4182	14	55	localisation	localisation	NOUN
ap-4182	14	56	at	at	ADP
ap-4182	14	57	edges	edge	NOUN
ap-4182	14	58	or	or	CCONJ
ap-4182	14	59	interfaces	interface	NOUN
ap-4182	14	60	of	of	ADP
ap-4182	14	61	the	the	DET
ap-4182	14	62	systems	system	NOUN
ap-4182	14	63	[	[	X
ap-4182	14	64	26	26	NUM
ap-4182	14	65	,	,	PUNCT
ap-4182	14	66	28	28	NUM
ap-4182	14	67	–	–	PUNCT
ap-4182	14	68	30	30	NUM
ap-4182	14	69	,	,	PUNCT
ap-4182	14	70	32	32	NUM
ap-4182	14	71	]	]	PUNCT
ap-4182	14	72	.	.	PUNCT
ap-4182	15	1	the	the	DET
ap-4182	15	2	identification	identification	NOUN
ap-4182	15	3	and	and	CCONJ
ap-4182	15	4	calculation	calculation	NOUN
ap-4182	15	5	of	of	ADP
ap-4182	15	6	topological	topological	ADJ
ap-4182	15	7	invariants	invariant	NOUN
ap-4182	15	8	such	such	ADJ
ap-4182	15	9	as	as	ADP
ap-4182	15	10	the	the	DET
ap-4182	15	11	zak	zak	PROPN
ap-4182	15	12	phase	phase	NOUN
ap-4182	15	13	[	[	X
ap-4182	15	14	36	36	NUM
ap-4182	15	15	]	]	PUNCT
ap-4182	15	16	known	know	VERB
ap-4182	15	17	from	from	ADP
ap-4182	15	18	hermitian	hermitian	ADJ
ap-4182	15	19	systems	system	NOUN
ap-4182	15	20	leads	lead	VERB
ap-4182	15	21	to	to	ADP
ap-4182	15	22	new	new	ADJ
ap-4182	15	23	challenges	challenge	NOUN
ap-4182	15	24	in	in	ADP
ap-4182	15	25	the	the	DET
ap-4182	15	26	case	case	NOUN
ap-4182	15	27	of	of	ADP
ap-4182	15	28	non	non	ADJ
ap-4182	15	29	-	-	ADJ
ap-4182	15	30	hermitian	hermitian	ADJ
ap-4182	15	31	operators	operator	NOUN
ap-4182	15	32	[	[	X
ap-4182	15	33	27	27	NUM
ap-4182	15	34	,	,	PUNCT
ap-4182	15	35	37	37	NUM
ap-4182	15	36	,	,	PUNCT
ap-4182	15	37	38	38	NUM
ap-4182	15	38	]	]	PUNCT
ap-4182	15	39	.	.	PUNCT
ap-4182	16	1	this	this	PRON
ap-4182	16	2	is	be	AUX
ap-4182	16	3	especially	especially	ADV
ap-4182	16	4	true	true	ADJ
ap-4182	16	5	if	if	SCONJ
ap-4182	16	6	the	the	DET
ap-4182	16	7	eigenstates	eigenstate	NOUN
ap-4182	16	8	are	be	AUX
ap-4182	16	9	only	only	ADV
ap-4182	16	10	available	available	ADJ
ap-4182	16	11	numerically	numerically	ADV
ap-4182	16	12	.	.	PUNCT
ap-4182	17	1	indeed	indeed	ADV
ap-4182	17	2	,	,	PUNCT
ap-4182	17	3	in	in	ADP
ap-4182	17	4	refs	ref	NOUN
ap-4182	17	5	.	.	PUNCT
ap-4182	18	1	[	[	X
ap-4182	18	2	27	27	NUM
ap-4182	18	3	,	,	PUNCT
ap-4182	18	4	37	37	NUM
ap-4182	18	5	,	,	PUNCT
ap-4182	18	6	38	38	NUM
ap-4182	18	7	]	]	PUNCT
ap-4182	18	8	all	all	DET
ap-4182	18	9	calculations	calculation	NOUN
ap-4182	18	10	have	have	AUX
ap-4182	18	11	been	be	AUX
ap-4182	18	12	done	do	VERB
ap-4182	18	13	for	for	ADP
ap-4182	18	14	eigenstates	eigenstate	NOUN
ap-4182	18	15	which	which	PRON
ap-4182	18	16	are	be	AUX
ap-4182	18	17	analytically	analytically	ADV
ap-4182	18	18	available	available	ADJ
ap-4182	18	19	.	.	PUNCT
ap-4182	19	1	however	however	ADV
ap-4182	19	2	,	,	PUNCT
ap-4182	19	3	for	for	ADP
ap-4182	19	4	arbitrary	arbitrary	ADJ
ap-4182	19	5	pt	pt	ADJ
ap-4182	19	6	-symmetric	-symmetric	ADJ
ap-4182	19	7	complex	complex	NOUN
ap-4182	19	8	potentials	potential	VERB
ap-4182	19	9	analytical	analytical	ADJ
ap-4182	19	10	access	access	NOUN
ap-4182	19	11	to	to	ADP
ap-4182	19	12	the	the	DET
ap-4182	19	13	eigenstates	eigenstate	NOUN
ap-4182	19	14	is	be	AUX
ap-4182	19	15	not	not	PART
ap-4182	19	16	available	available	ADJ
ap-4182	19	17	and	and	CCONJ
ap-4182	19	18	a	a	DET
ap-4182	19	19	reliable	reliable	ADJ
ap-4182	19	20	numerical	numerical	ADJ
ap-4182	19	21	procedure	procedure	NOUN
ap-4182	19	22	is	be	AUX
ap-4182	19	23	required	require	VERB
ap-4182	19	24	.	.	PUNCT
ap-4182	20	1	for	for	ADP
ap-4182	20	2	the	the	DET
ap-4182	20	3	calculation	calculation	NOUN
ap-4182	20	4	of	of	ADP
ap-4182	20	5	the	the	DET
ap-4182	20	6	invariants	invariant	NOUN
ap-4182	20	7	an	an	DET
ap-4182	20	8	integration	integration	NOUN
ap-4182	20	9	of	of	ADP
ap-4182	20	10	phases	phase	NOUN
ap-4182	20	11	over	over	ADP
ap-4182	20	12	a	a	DET
ap-4182	20	13	loop	loop	NOUN
ap-4182	20	14	in	in	ADP
ap-4182	20	15	parameter	parameter	NOUN
ap-4182	20	16	space	space	NOUN
ap-4182	20	17	is	be	AUX
ap-4182	20	18	typically	typically	ADV
ap-4182	20	19	necessary	necessary	ADJ
ap-4182	20	20	.	.	PUNCT
ap-4182	21	1	for	for	ADP
ap-4182	21	2	example	example	NOUN
ap-4182	21	3	,	,	PUNCT
ap-4182	21	4	in	in	ADP
ap-4182	21	5	the	the	DET
ap-4182	21	6	case	case	NOUN
ap-4182	21	7	of	of	ADP
ap-4182	21	8	the	the	DET
ap-4182	21	9	zak	zak	PROPN
ap-4182	21	10	phase	phase	NOUN
ap-4182	21	11	,	,	PUNCT
ap-4182	21	12	which	which	PRON
ap-4182	21	13	is	be	AUX
ap-4182	21	14	applied	apply	VERB
ap-4182	21	15	to	to	ADP
ap-4182	21	16	one	one	NUM
ap-4182	21	17	-	-	PUNCT
ap-4182	21	18	dimensional	dimensional	ADJ
ap-4182	21	19	systems	system	NOUN
ap-4182	21	20	,	,	PUNCT
ap-4182	21	21	this	this	DET
ap-4182	21	22	integral	integral	ADJ
ap-4182	21	23	runs	run	NOUN
ap-4182	21	24	over	over	ADP
ap-4182	21	25	the	the	DET
ap-4182	21	26	first	first	ADJ
ap-4182	21	27	brillouin	brillouin	NOUN
ap-4182	21	28	zone	zone	NOUN
ap-4182	21	29	.	.	PUNCT
ap-4182	22	1	the	the	DET
ap-4182	22	2	integrand	integrand	PROPN
ap-4182	22	3	contains	contain	VERB
ap-4182	22	4	the	the	DET
ap-4182	22	5	eigenstates	eigenstate	NOUN
ap-4182	22	6	of	of	ADP
ap-4182	22	7	the	the	DET
ap-4182	22	8	hamiltonian	hamiltonian	NOUN
ap-4182	22	9	and	and	CCONJ
ap-4182	22	10	their	their	PRON
ap-4182	22	11	first	first	ADJ
ap-4182	22	12	derivatives	derivative	NOUN
ap-4182	22	13	.	.	PUNCT
ap-4182	23	1	in	in	ADP
ap-4182	23	2	a	a	DET
ap-4182	23	3	numerical	numerical	ADJ
ap-4182	23	4	calculation	calculation	NOUN
ap-4182	23	5	it	it	PRON
ap-4182	23	6	is	be	AUX
ap-4182	23	7	evaluated	evaluate	VERB
ap-4182	23	8	at	at	ADP
ap-4182	23	9	discrete	discrete	ADJ
ap-4182	23	10	points	point	NOUN
ap-4182	23	11	in	in	ADP
ap-4182	23	12	momentum	momentum	NOUN
ap-4182	23	13	space	space	NOUN
ap-4182	23	14	and	and	CCONJ
ap-4182	23	15	each	each	DET
ap-4182	23	16	state	state	NOUN
ap-4182	23	17	possesses	possess	VERB
ap-4182	23	18	an	an	DET
ap-4182	23	19	arbitrary	arbitrary	ADJ
ap-4182	23	20	global	global	ADJ
ap-4182	23	21	phase	phase	NOUN
ap-4182	23	22	spoiling	spoil	VERB
ap-4182	23	23	the	the	DET
ap-4182	23	24	phase	phase	NOUN
ap-4182	23	25	relation	relation	NOUN
ap-4182	23	26	.	.	PUNCT
ap-4182	24	1	this	this	PRON
ap-4182	24	2	is	be	AUX
ap-4182	24	3	the	the	DET
ap-4182	24	4	point	point	NOUN
ap-4182	24	5	our	our	PRON
ap-4182	24	6	study	study	NOUN
ap-4182	24	7	sets	set	VERB
ap-4182	24	8	in	in	ADP
ap-4182	24	9	.	.	PUNCT
ap-4182	25	1	in	in	ADP
ap-4182	25	2	this	this	DET
ap-4182	25	3	article	article	NOUN
ap-4182	25	4	we	we	PRON
ap-4182	25	5	introduce	introduce	VERB
ap-4182	25	6	a	a	DET
ap-4182	25	7	robust	robust	ADJ
ap-4182	25	8	method	method	NOUN
ap-4182	25	9	of	of	ADP
ap-4182	25	10	calculating	calculate	VERB
ap-4182	25	11	the	the	DET
ap-4182	25	12	complex	complex	ADJ
ap-4182	25	13	berry	berry	NOUN
ap-4182	25	14	phase	phase	NOUN
ap-4182	25	15	numerically	numerically	ADV
ap-4182	25	16	.	.	PUNCT
ap-4182	26	1	it	it	PRON
ap-4182	26	2	is	be	AUX
ap-4182	26	3	based	base	VERB
ap-4182	26	4	on	on	ADP
ap-4182	26	5	a	a	DET
ap-4182	26	6	normalisation	normalisation	NOUN
ap-4182	26	7	of	of	ADP
ap-4182	26	8	the	the	DET
ap-4182	26	9	leftand	leftand	NOUN
ap-4182	26	10	right	right	ADJ
ap-4182	26	11	-	-	PUNCT
ap-4182	26	12	hand	hand	NOUN
ap-4182	26	13	eigenvectors	eigenvector	NOUN
ap-4182	26	14	with	with	ADP
ap-4182	26	15	the	the	DET
ap-4182	26	16	biorthogonal	biorthogonal	ADJ
ap-4182	26	17	inner	inner	ADJ
ap-4182	26	18	product	product	NOUN
ap-4182	26	19	[	[	X
ap-4182	26	20	39	39	NUM
ap-4182	26	21	]	]	PUNCT
ap-4182	26	22	,	,	PUNCT
ap-4182	26	23	which	which	PRON
ap-4182	26	24	reduces	reduce	VERB
ap-4182	26	25	to	to	ADP
ap-4182	26	26	the	the	DET
ap-4182	26	27	c	c	NOUN
ap-4182	26	28	product	product	NOUN
ap-4182	26	29	[	[	X
ap-4182	26	30	40	40	NUM
ap-4182	26	31	]	]	PUNCT
ap-4182	26	32	in	in	ADP
ap-4182	26	33	the	the	DET
ap-4182	26	34	case	case	NOUN
ap-4182	26	35	of	of	ADP
ap-4182	26	36	complex	complex	ADJ
ap-4182	26	37	symmetric	symmetric	ADJ
ap-4182	26	38	hamiltonians	hamiltonian	NOUN
ap-4182	26	39	.	.	PUNCT
ap-4182	27	1	to	to	PART
ap-4182	27	2	obtain	obtain	VERB
ap-4182	27	3	an	an	DET
ap-4182	27	4	unambiguous	unambiguous	ADJ
ap-4182	27	5	complex	complex	ADJ
ap-4182	27	6	berry	berry	NOUN
ap-4182	27	7	phase	phase	NOUN
ap-4182	27	8	we	we	PRON
ap-4182	27	9	introduce	introduce	VERB
ap-4182	27	10	a	a	DET
ap-4182	27	11	numerical	numerical	ADJ
ap-4182	27	12	gauge	gauge	NOUN
ap-4182	27	13	smoothing	smoothing	NOUN
ap-4182	27	14	procedure	procedure	NOUN
ap-4182	27	15	.	.	PUNCT
ap-4182	28	1	it	it	PRON
ap-4182	28	2	consists	consist	VERB
ap-4182	28	3	of	of	ADP
ap-4182	28	4	two	two	NUM
ap-4182	28	5	parts	part	NOUN
ap-4182	28	6	.	.	PUNCT
ap-4182	29	1	first	first	ADV
ap-4182	29	2	we	we	PRON
ap-4182	29	3	have	have	VERB
ap-4182	29	4	to	to	PART
ap-4182	29	5	remove	remove	VERB
ap-4182	29	6	the	the	DET
ap-4182	29	7	influence	influence	NOUN
ap-4182	29	8	of	of	ADP
ap-4182	29	9	the	the	DET
ap-4182	29	10	arbitrary	arbitrary	ADJ
ap-4182	29	11	and	and	CCONJ
ap-4182	29	12	unconnected	unconnected	ADJ
ap-4182	29	13	global	global	ADJ
ap-4182	29	14	phases	phase	NOUN
ap-4182	29	15	of	of	ADP
ap-4182	29	16	the	the	DET
ap-4182	29	17	eigenstates	eigenstate	NOUN
ap-4182	29	18	,	,	PUNCT
ap-4182	29	19	which	which	PRON
ap-4182	29	20	is	be	AUX
ap-4182	29	21	unavoidably	unavoidably	ADV
ap-4182	29	22	attached	attach	VERB
ap-4182	29	23	to	to	ADP
ap-4182	29	24	them	they	PRON
ap-4182	29	25	for	for	ADP
ap-4182	29	26	each	each	DET
ap-4182	29	27	point	point	NOUN
ap-4182	29	28	in	in	ADP
ap-4182	29	29	parameter	parameter	NOUN
ap-4182	29	30	space	space	NOUN
ap-4182	29	31	.	.	PUNCT
ap-4182	30	1	this	this	PRON
ap-4182	30	2	is	be	AUX
ap-4182	30	3	achieved	achieve	VERB
ap-4182	30	4	by	by	ADP
ap-4182	30	5	relating	relate	VERB
ap-4182	30	6	the	the	DET
ap-4182	30	7	eigenvectors	eigenvector	NOUN
ap-4182	30	8	of	of	ADP
ap-4182	30	9	consecutive	consecutive	ADJ
ap-4182	30	10	steps	step	NOUN
ap-4182	30	11	in	in	ADP
ap-4182	30	12	parameter	parameter	NOUN
ap-4182	30	13	space	space	NOUN
ap-4182	30	14	,	,	PUNCT
ap-4182	30	15	and	and	CCONJ
ap-4182	30	16	then	then	ADV
ap-4182	30	17	normalising	normalise	VERB
ap-4182	30	18	them	they	PRON
ap-4182	30	19	.	.	PUNCT
ap-4182	31	1	with	with	ADP
ap-4182	31	2	this	this	DET
ap-4182	31	3	approach	approach	NOUN
ap-4182	31	4	the	the	DET
ap-4182	31	5	eigenvectors	eigenvector	NOUN
ap-4182	31	6	are	be	AUX
ap-4182	31	7	not	not	PART
ap-4182	31	8	yet	yet	ADV
ap-4182	31	9	single	single	ADV
ap-4182	31	10	-	-	PUNCT
ap-4182	31	11	valued	value	VERB
ap-4182	31	12	,	,	PUNCT
ap-4182	31	13	i.e.	i.e.	X
ap-4182	31	14	the	the	DET
ap-4182	31	15	vectors	vector	NOUN
ap-4182	31	16	at	at	ADP
ap-4182	31	17	the	the	DET
ap-4182	31	18	starting	starting	NOUN
ap-4182	31	19	and	and	CCONJ
ap-4182	31	20	end	end	VERB
ap-4182	31	21	point	point	NOUN
ap-4182	31	22	of	of	ADP
ap-4182	31	23	the	the	DET
ap-4182	31	24	loop	loop	NOUN
ap-4182	31	25	possess	possess	VERB
ap-4182	31	26	different	different	ADJ
ap-4182	31	27	phases	phase	NOUN
ap-4182	31	28	.	.	PUNCT
ap-4182	32	1	these	these	DET
ap-4182	32	2	points	point	NOUN
ap-4182	32	3	have	have	VERB
ap-4182	32	4	to	to	PART
ap-4182	32	5	be	be	AUX
ap-4182	32	6	identified	identify	VERB
ap-4182	32	7	and	and	CCONJ
ap-4182	32	8	will	will	AUX
ap-4182	32	9	be	be	AUX
ap-4182	32	10	refered	refer	VERB
ap-4182	32	11	as	as	ADP
ap-4182	32	12	the	the	DET
ap-4182	32	13	basepoint	basepoint	NOUN
ap-4182	32	14	of	of	ADP
ap-4182	32	15	the	the	DET
ap-4182	32	16	loop	loop	NOUN
ap-4182	32	17	later	later	ADV
ap-4182	32	18	on	on	ADV
ap-4182	32	19	.	.	PUNCT
ap-4182	33	1	the	the	DET
ap-4182	33	2	phase	phase	NOUN
ap-4182	33	3	difference	difference	NOUN
ap-4182	33	4	between	between	ADP
ap-4182	33	5	the	the	DET
ap-4182	33	6	different	different	ADJ
ap-4182	33	7	left	left	NOUN
ap-4182	33	8	and	and	CCONJ
ap-4182	33	9	right	right	ADJ
ap-4182	33	10	states	state	NOUN
ap-4182	33	11	at	at	ADP
ap-4182	33	12	the	the	DET
ap-4182	33	13	basepoint	basepoint	PROPN
ap-4182	33	14	has	have	VERB
ap-4182	33	15	to	to	PART
ap-4182	33	16	be	be	AUX
ap-4182	33	17	corrected	correct	VERB
ap-4182	33	18	by	by	ADP
ap-4182	33	19	ensuring	ensure	VERB
ap-4182	33	20	the	the	DET
ap-4182	33	21	eigenvectors	eigenvector	NOUN
ap-4182	33	22	to	to	PART
ap-4182	33	23	be	be	AUX
ap-4182	33	24	identical	identical	ADJ
ap-4182	33	25	at	at	ADP
ap-4182	33	26	the	the	DET
ap-4182	33	27	basepoint	basepoint	PROPN
ap-4182	33	28	.	.	PUNCT
ap-4182	34	1	the	the	DET
ap-4182	34	2	article	article	NOUN
ap-4182	34	3	is	be	AUX
ap-4182	34	4	organised	organise	VERB
ap-4182	34	5	as	as	SCONJ
ap-4182	34	6	follows	follow	VERB
ap-4182	34	7	.	.	PUNCT
ap-4182	35	1	first	first	ADV
ap-4182	35	2	,	,	PUNCT
ap-4182	35	3	we	we	PRON
ap-4182	35	4	introduce	introduce	VERB
ap-4182	35	5	the	the	DET
ap-4182	35	6	complex	complex	ADJ
ap-4182	35	7	berry	berry	NOUN
ap-4182	35	8	phase	phase	NOUN
ap-4182	35	9	in	in	ADP
ap-4182	35	10	section	section	NOUN
ap-4182	35	11	2	2	NUM
ap-4182	35	12	.	.	PUNCT
ap-4182	36	1	in	in	ADP
ap-4182	36	2	section	section	NOUN
ap-4182	36	3	470	470	NUM
ap-4182	36	4	http://dx.doi.org/10.14311/ap.2017.57.0470	http://dx.doi.org/10.14311/ap.2017.57.0470	ADP
ap-4182	36	5	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4182	36	6	vol	vol	NOUN
ap-4182	36	7	.	.	PUNCT
ap-4182	36	8	57	57	NUM
ap-4182	36	9	no	no	NOUN
ap-4182	36	10	.	.	PUNCT
ap-4182	37	1	6/2017	6/2017	NUM
ap-4182	37	2	numerical	numerical	ADJ
ap-4182	37	3	calculation	calculation	NOUN
ap-4182	37	4	of	of	ADP
ap-4182	37	5	the	the	DET
ap-4182	37	6	complex	complex	ADJ
ap-4182	37	7	berry	berry	NOUN
ap-4182	37	8	phase	phase	NOUN
ap-4182	37	9	3	3	NUM
ap-4182	37	10	we	we	PRON
ap-4182	37	11	establish	establish	VERB
ap-4182	37	12	the	the	DET
ap-4182	37	13	algorithm	algorithm	NOUN
ap-4182	37	14	of	of	ADP
ap-4182	37	15	the	the	DET
ap-4182	37	16	gauge	gauge	NOUN
ap-4182	37	17	smoothing	smoothing	NOUN
ap-4182	37	18	procedure	procedure	NOUN
ap-4182	37	19	for	for	ADP
ap-4182	37	20	non	non	ADJ
ap-4182	37	21	-	-	ADJ
ap-4182	37	22	hermitian	hermitian	ADJ
ap-4182	37	23	(	(	PUNCT
ap-4182	37	24	and	and	CCONJ
ap-4182	37	25	hermitian	hermitian	ADJ
ap-4182	37	26	)	)	PUNCT
ap-4182	37	27	hamiltonians	hamiltonian	NOUN
ap-4182	37	28	.	.	PUNCT
ap-4182	38	1	an	an	DET
ap-4182	38	2	example	example	NOUN
ap-4182	38	3	is	be	AUX
ap-4182	38	4	presented	present	VERB
ap-4182	38	5	in	in	ADP
ap-4182	38	6	section	section	NOUN
ap-4182	38	7	4	4	NUM
ap-4182	38	8	,	,	PUNCT
ap-4182	38	9	where	where	SCONJ
ap-4182	38	10	we	we	PRON
ap-4182	38	11	apply	apply	VERB
ap-4182	38	12	the	the	DET
ap-4182	38	13	previously	previously	ADV
ap-4182	38	14	developed	develop	VERB
ap-4182	38	15	method	method	NOUN
ap-4182	38	16	to	to	ADP
ap-4182	38	17	a	a	DET
ap-4182	38	18	nonhermitian	nonhermitian	ADJ
ap-4182	38	19	extension	extension	NOUN
ap-4182	38	20	of	of	ADP
ap-4182	38	21	the	the	DET
ap-4182	38	22	su	su	PROPN
ap-4182	38	23	-	-	PUNCT
ap-4182	38	24	schrieffer	schrieffer	NOUN
ap-4182	38	25	-	-	PUNCT
ap-4182	38	26	heeger	heeger	NOUN
ap-4182	38	27	(	(	PUNCT
ap-4182	38	28	ssh	ssh	NOUN
ap-4182	38	29	)	)	PUNCT
ap-4182	38	30	model	model	NOUN
ap-4182	39	1	[	[	X
ap-4182	39	2	41	41	NUM
ap-4182	39	3	]	]	PUNCT
ap-4182	39	4	to	to	PART
ap-4182	39	5	calculate	calculate	VERB
ap-4182	39	6	its	its	PRON
ap-4182	39	7	complex	complex	ADJ
ap-4182	39	8	zak	zak	PROPN
ap-4182	39	9	phase	phase	NOUN
ap-4182	39	10	.	.	PUNCT
ap-4182	40	1	2	2	X
ap-4182	40	2	.	.	X
ap-4182	40	3	complex	complex	ADJ
ap-4182	40	4	berry	berry	NOUN
ap-4182	40	5	phase	phase	NOUN
ap-4182	40	6	topological	topological	ADJ
ap-4182	40	7	phases	phase	NOUN
ap-4182	40	8	of	of	ADP
ap-4182	40	9	closed	close	VERB
ap-4182	40	10	one	one	NUM
ap-4182	40	11	-	-	PUNCT
ap-4182	40	12	dimensional	dimensional	ADJ
ap-4182	40	13	periodic	periodic	ADJ
ap-4182	40	14	lattice	lattice	NOUN
ap-4182	40	15	systems	system	NOUN
ap-4182	40	16	are	be	AUX
ap-4182	40	17	characterised	characterise	VERB
ap-4182	40	18	by	by	ADP
ap-4182	40	19	the	the	DET
ap-4182	40	20	zak	zak	PROPN
ap-4182	40	21	phase	phase	NOUN
ap-4182	40	22	[	[	X
ap-4182	40	23	36	36	NUM
ap-4182	40	24	]	]	X
ap-4182	40	25	,	,	PUNCT
ap-4182	40	26	which	which	PRON
ap-4182	40	27	is	be	AUX
ap-4182	40	28	the	the	DET
ap-4182	40	29	berry	berry	NOUN
ap-4182	40	30	phase	phase	NOUN
ap-4182	41	1	[	[	X
ap-4182	41	2	42	42	NUM
ap-4182	41	3	]	]	PUNCT
ap-4182	41	4	picked	pick	VERB
ap-4182	41	5	up	up	ADP
ap-4182	41	6	by	by	ADP
ap-4182	41	7	the	the	DET
ap-4182	41	8	eigenstate	eigenstate	NOUN
ap-4182	41	9	when	when	SCONJ
ap-4182	41	10	it	it	PRON
ap-4182	41	11	is	be	AUX
ap-4182	41	12	transported	transport	VERB
ap-4182	41	13	once	once	ADV
ap-4182	41	14	along	along	ADP
ap-4182	41	15	the	the	DET
ap-4182	41	16	brillouin	brillouin	NOUN
ap-4182	41	17	zone	zone	NOUN
ap-4182	41	18	.	.	PUNCT
ap-4182	42	1	in	in	ADP
ap-4182	42	2	the	the	DET
ap-4182	42	3	presence	presence	NOUN
ap-4182	42	4	of	of	ADP
ap-4182	42	5	an	an	DET
ap-4182	42	6	antiunitary	antiunitary	ADJ
ap-4182	42	7	symmetry	symmetry	NOUN
ap-4182	42	8	these	these	DET
ap-4182	42	9	phases	phase	NOUN
ap-4182	42	10	are	be	AUX
ap-4182	42	11	quantised	quantise	VERB
ap-4182	42	12	[	[	X
ap-4182	42	13	43	43	NUM
ap-4182	42	14	]	]	PUNCT
ap-4182	42	15	and	and	CCONJ
ap-4182	42	16	can	can	AUX
ap-4182	42	17	be	be	AUX
ap-4182	42	18	related	relate	VERB
ap-4182	42	19	to	to	ADP
ap-4182	42	20	the	the	DET
ap-4182	42	21	winding	wind	VERB
ap-4182	42	22	number	number	NOUN
ap-4182	42	23	of	of	ADP
ap-4182	42	24	a	a	DET
ap-4182	42	25	vector	vector	NOUN
ap-4182	42	26	n(k	n(k	PROPN
ap-4182	42	27	)	)	PUNCT
ap-4182	42	28	determining	determine	VERB
ap-4182	42	29	the	the	DET
ap-4182	42	30	bloch	bloch	PROPN
ap-4182	42	31	hamiltonian	hamiltonian	NOUN
ap-4182	42	32	h(k	h(k	PROPN
ap-4182	42	33	)	)	PUNCT
ap-4182	43	1	=	=	SYM
ap-4182	43	2	n(k	n(k	PROPN
ap-4182	43	3	)	)	PUNCT
ap-4182	43	4	·	·	PUNCT
ap-4182	44	1	σ	σ	X
ap-4182	44	2	,	,	PUNCT
ap-4182	44	3	(	(	PUNCT
ap-4182	44	4	1	1	X
ap-4182	44	5	)	)	PUNCT
ap-4182	44	6	where	where	SCONJ
ap-4182	44	7	σ	σ	PROPN
ap-4182	44	8	denotes	denote	VERB
ap-4182	44	9	the	the	DET
ap-4182	44	10	vector	vector	NOUN
ap-4182	44	11	of	of	ADP
ap-4182	44	12	pauli	pauli	PROPN
ap-4182	44	13	matrices	matrix	NOUN
ap-4182	44	14	and	and	CCONJ
ap-4182	44	15	k	k	PROPN
ap-4182	44	16	is	be	AUX
ap-4182	44	17	the	the	DET
ap-4182	44	18	wave	wave	NOUN
ap-4182	44	19	number	number	NOUN
ap-4182	44	20	parametrising	parametrise	VERB
ap-4182	44	21	the	the	DET
ap-4182	44	22	brillouin	brillouin	NOUN
ap-4182	44	23	zone	zone	NOUN
ap-4182	44	24	,	,	PUNCT
ap-4182	44	25	which	which	PRON
ap-4182	44	26	acts	act	VERB
ap-4182	44	27	as	as	ADP
ap-4182	44	28	parameter	parameter	NOUN
ap-4182	44	29	space	space	NOUN
ap-4182	44	30	.	.	PUNCT
ap-4182	45	1	in	in	ADP
ap-4182	45	2	this	this	DET
ap-4182	45	3	case	case	NOUN
ap-4182	45	4	the	the	DET
ap-4182	45	5	zak	zak	PROPN
ap-4182	45	6	phase	phase	NOUN
ap-4182	45	7	characterises	characterise	VERB
ap-4182	45	8	the	the	DET
ap-4182	45	9	system	system	NOUN
ap-4182	45	10	’s	’s	PART
ap-4182	45	11	topological	topological	ADJ
ap-4182	45	12	phase	phase	NOUN
ap-4182	45	13	.	.	PUNCT
ap-4182	46	1	this	this	DET
ap-4182	46	2	concept	concept	NOUN
ap-4182	46	3	can	can	AUX
ap-4182	46	4	be	be	AUX
ap-4182	46	5	generalised	generalise	VERB
ap-4182	46	6	to	to	ADP
ap-4182	46	7	dissipative	dissipative	ADJ
ap-4182	46	8	systems	system	NOUN
ap-4182	46	9	effectively	effectively	ADV
ap-4182	46	10	described	describe	VERB
ap-4182	46	11	by	by	ADP
ap-4182	46	12	a	a	DET
ap-4182	46	13	pt	pt	NOUN
ap-4182	46	14	-symmetric	-symmetric	ADJ
ap-4182	46	15	nonhermitian	nonhermitian	ADJ
ap-4182	46	16	hamiltonian	hamiltonian	NOUN
ap-4182	46	17	h(α	h(α	PROPN
ap-4182	46	18	)	)	PUNCT
ap-4182	46	19	.	.	PUNCT
ap-4182	47	1	the	the	DET
ap-4182	47	2	complex	complex	ADJ
ap-4182	47	3	berry	berry	NOUN
ap-4182	47	4	phase	phase	NOUN
ap-4182	47	5	γn	γn	ADP
ap-4182	47	6	of	of	ADP
ap-4182	47	7	a	a	DET
ap-4182	47	8	biorthogonal	biorthogonal	ADJ
ap-4182	47	9	pair	pair	NOUN
ap-4182	47	10	of	of	ADP
ap-4182	47	11	eigenvectors	eigenvector	NOUN
ap-4182	47	12	〈	〈	PROPN
ap-4182	47	13	χn|	χn|	PROPN
ap-4182	47	14	and	and	CCONJ
ap-4182	47	15	|φn	|φn	NOUN
ap-4182	47	16	〉	〉	NOUN
ap-4182	47	17	of	of	ADP
ap-4182	47	18	h(α	h(α	PROPN
ap-4182	47	19	)	)	PUNCT
ap-4182	47	20	,	,	PUNCT
ap-4182	47	21	γn	γn	X
ap-4182	47	22	=	=	VERB
ap-4182	47	23	i	i	PRON
ap-4182	47	24	∮	∮	PRON
ap-4182	47	25	c	c	VERB
ap-4182	47	26	〈	〈	PROPN
ap-4182	47	27	χn|∇α|φn	χn|∇α|φn	PROPN
ap-4182	47	28	〉	〉	PROPN
ap-4182	47	29	·	·	PUNCT
ap-4182	47	30	dα	dα	NOUN
ap-4182	47	31	,	,	PUNCT
ap-4182	47	32	(	(	PUNCT
ap-4182	47	33	2	2	X
ap-4182	47	34	)	)	PUNCT
ap-4182	47	35	follows	follow	VERB
ap-4182	47	36	from	from	ADP
ap-4182	47	37	the	the	DET
ap-4182	47	38	lowest	low	ADJ
ap-4182	47	39	order	order	NOUN
ap-4182	47	40	of	of	ADP
ap-4182	47	41	the	the	DET
ap-4182	47	42	adiabatic	adiabatic	ADJ
ap-4182	47	43	approximation	approximation	NOUN
ap-4182	47	44	of	of	ADP
ap-4182	47	45	the	the	DET
ap-4182	47	46	time	time	NOUN
ap-4182	47	47	evolution	evolution	NOUN
ap-4182	47	48	of	of	ADP
ap-4182	47	49	a	a	DET
ap-4182	47	50	state	state	NOUN
ap-4182	47	51	in	in	ADP
ap-4182	47	52	parameter	parameter	NOUN
ap-4182	47	53	space	space	NOUN
ap-4182	47	54	[	[	X
ap-4182	47	55	44	44	NUM
ap-4182	47	56	]	]	PUNCT
ap-4182	47	57	.	.	PUNCT
ap-4182	48	1	here	here	ADV
ap-4182	48	2	c	c	PROPN
ap-4182	48	3	is	be	AUX
ap-4182	48	4	a	a	DET
ap-4182	48	5	loop	loop	NOUN
ap-4182	48	6	in	in	ADP
ap-4182	48	7	parameter	parameter	NOUN
ap-4182	48	8	space	space	NOUN
ap-4182	48	9	and	and	CCONJ
ap-4182	48	10	α	α	NOUN
ap-4182	48	11	=	=	SYM
ap-4182	48	12	(	(	PUNCT
ap-4182	48	13	α1	α1	PROPN
ap-4182	48	14	,	,	PUNCT
ap-4182	48	15	...	...	PUNCT
ap-4182	48	16	,	,	PUNCT
ap-4182	48	17	αi	αi	PROPN
ap-4182	48	18	,	,	PUNCT
ap-4182	48	19	...	...	PUNCT
ap-4182	48	20	)	)	PUNCT
ap-4182	48	21	are	be	AUX
ap-4182	48	22	its	its	PRON
ap-4182	48	23	coordinates	coordinate	NOUN
ap-4182	48	24	.	.	PUNCT
ap-4182	49	1	we	we	PRON
ap-4182	49	2	consider	consider	VERB
ap-4182	49	3	pt	pt	X
ap-4182	49	4	-symmetric	-symmetric	ADJ
ap-4182	49	5	non	non	ADJ
ap-4182	49	6	-	-	ADJ
ap-4182	49	7	hermitian	hermitian	ADJ
ap-4182	49	8	hamiltonians	hamiltonian	NOUN
ap-4182	49	9	of	of	ADP
ap-4182	49	10	the	the	DET
ap-4182	49	11	form	form	NOUN
ap-4182	49	12	h(α	h(α	ADJ
ap-4182	49	13	)	)	PUNCT
ap-4182	49	14	=	=	SYM
ap-4182	49	15	hh(α	hh(α	X
ap-4182	49	16	)	)	PUNCT
ap-4182	50	1	+	+	NOUN
ap-4182	50	2	hnh(α	hnh(α	NOUN
ap-4182	50	3	)	)	PUNCT
ap-4182	50	4	,	,	PUNCT
ap-4182	50	5	(	(	PUNCT
ap-4182	50	6	3	3	X
ap-4182	50	7	)	)	PUNCT
ap-4182	50	8	where	where	SCONJ
ap-4182	50	9	hh	hh	PROPN
ap-4182	50	10	denotes	denote	VERB
ap-4182	50	11	its	its	PRON
ap-4182	50	12	hermitian	hermitian	NOUN
ap-4182	50	13	and	and	CCONJ
ap-4182	50	14	hnh	hnh	NOUN
ap-4182	50	15	represents	represent	VERB
ap-4182	50	16	its	its	PRON
ap-4182	50	17	pt	pt	NOUN
ap-4182	50	18	-symmetric	-symmetric	ADJ
ap-4182	50	19	non	non	ADJ
ap-4182	50	20	-	-	ADJ
ap-4182	50	21	hermitian	hermitian	ADJ
ap-4182	50	22	part	part	NOUN
ap-4182	50	23	.	.	PUNCT
ap-4182	51	1	the	the	DET
ap-4182	51	2	nonhermitian	nonhermitian	ADJ
ap-4182	51	3	part	part	NOUN
ap-4182	51	4	is	be	AUX
ap-4182	51	5	a	a	DET
ap-4182	51	6	complex	complex	ADJ
ap-4182	51	7	potential	potential	NOUN
ap-4182	51	8	modelling	model	VERB
ap-4182	51	9	the	the	DET
ap-4182	51	10	gain	gain	NOUN
ap-4182	51	11	and	and	CCONJ
ap-4182	51	12	loss	loss	NOUN
ap-4182	51	13	of	of	ADP
ap-4182	51	14	particles	particle	NOUN
ap-4182	51	15	.	.	PUNCT
ap-4182	52	1	the	the	DET
ap-4182	52	2	complex	complex	ADJ
ap-4182	52	3	berry	berry	NOUN
ap-4182	52	4	phase	phase	NOUN
ap-4182	52	5	γn	γn	ADP
ap-4182	52	6	arising	arise	VERB
ap-4182	52	7	from	from	ADP
ap-4182	52	8	the	the	DET
ap-4182	52	9	periodic	periodic	ADJ
ap-4182	52	10	modulation	modulation	NOUN
ap-4182	52	11	of	of	ADP
ap-4182	52	12	states	state	NOUN
ap-4182	52	13	in	in	ADP
ap-4182	52	14	the	the	DET
ap-4182	52	15	parameter	parameter	NOUN
ap-4182	52	16	space	space	NOUN
ap-4182	52	17	of	of	ADP
ap-4182	52	18	a	a	DET
ap-4182	52	19	pt	pt	NOUN
ap-4182	52	20	-symmetric	-symmetric	ADJ
ap-4182	52	21	one	one	NUM
ap-4182	52	22	-	-	PUNCT
ap-4182	52	23	dimensional	dimensional	ADJ
ap-4182	52	24	system	system	NOUN
ap-4182	52	25	can	can	AUX
ap-4182	52	26	not	not	PART
ap-4182	52	27	be	be	AUX
ap-4182	52	28	related	relate	VERB
ap-4182	52	29	to	to	ADP
ap-4182	52	30	a	a	DET
ap-4182	52	31	real	real	ADJ
ap-4182	52	32	winding	wind	VERB
ap-4182	52	33	number	number	NOUN
ap-4182	52	34	calculated	calculate	VERB
ap-4182	52	35	from	from	ADP
ap-4182	52	36	(	(	PUNCT
ap-4182	52	37	1	1	NUM
ap-4182	52	38	)	)	PUNCT
ap-4182	52	39	.	.	PUNCT
ap-4182	53	1	hence	hence	ADV
ap-4182	53	2	,	,	PUNCT
ap-4182	53	3	the	the	DET
ap-4182	53	4	calculation	calculation	NOUN
ap-4182	53	5	of	of	ADP
ap-4182	53	6	the	the	DET
ap-4182	53	7	complex	complex	ADJ
ap-4182	53	8	berry	berry	NOUN
ap-4182	53	9	phase	phase	NOUN
ap-4182	53	10	requires	require	VERB
ap-4182	53	11	the	the	DET
ap-4182	53	12	determination	determination	NOUN
ap-4182	53	13	of	of	ADP
ap-4182	53	14	gauge	gauge	NOUN
ap-4182	53	15	-	-	PUNCT
ap-4182	53	16	smoothed	smooth	VERB
ap-4182	53	17	eigenvector	eigenvector	NOUN
ap-4182	53	18	pairs	pair	NOUN
ap-4182	53	19	along	along	ADP
ap-4182	53	20	the	the	DET
ap-4182	53	21	loop	loop	NOUN
ap-4182	53	22	c	c	PROPN
ap-4182	53	23	in	in	ADP
ap-4182	53	24	parameter	parameter	NOUN
ap-4182	53	25	space	space	NOUN
ap-4182	53	26	allowing	allow	VERB
ap-4182	53	27	for	for	ADP
ap-4182	53	28	the	the	DET
ap-4182	53	29	evaluation	evaluation	NOUN
ap-4182	53	30	of	of	ADP
ap-4182	53	31	(	(	PUNCT
ap-4182	53	32	2	2	NUM
ap-4182	53	33	)	)	PUNCT
ap-4182	53	34	.	.	PUNCT
ap-4182	54	1	here	here	ADV
ap-4182	54	2	,	,	PUNCT
ap-4182	54	3	it	it	PRON
ap-4182	54	4	is	be	AUX
ap-4182	54	5	important	important	ADJ
ap-4182	54	6	to	to	PART
ap-4182	54	7	note	note	VERB
ap-4182	54	8	that	that	SCONJ
ap-4182	54	9	the	the	DET
ap-4182	54	10	argumentation	argumentation	NOUN
ap-4182	54	11	of	of	ADP
ap-4182	54	12	hatsugai	hatsugai	PROPN
ap-4182	54	13	[	[	X
ap-4182	54	14	43	43	NUM
ap-4182	54	15	]	]	PUNCT
ap-4182	54	16	for	for	ADP
ap-4182	54	17	the	the	DET
ap-4182	54	18	quantisation	quantisation	NOUN
ap-4182	54	19	of	of	ADP
ap-4182	54	20	berry	berry	NOUN
ap-4182	54	21	phases	phase	NOUN
ap-4182	54	22	of	of	ADP
ap-4182	54	23	hermitian	hermitian	ADJ
ap-4182	54	24	hamiltonians	hamiltonian	NOUN
ap-4182	54	25	can	can	AUX
ap-4182	54	26	be	be	AUX
ap-4182	54	27	extended	extend	VERB
ap-4182	54	28	on	on	ADP
ap-4182	54	29	complex	complex	ADJ
ap-4182	54	30	berry	berry	NOUN
ap-4182	54	31	phases	phase	NOUN
ap-4182	54	32	of	of	ADP
ap-4182	54	33	non	non	ADJ
ap-4182	54	34	-	-	ADJ
ap-4182	54	35	hermitian	hermitian	ADJ
ap-4182	54	36	pt	pt	X
ap-4182	54	37	-symmetric	-symmetric	ADJ
ap-4182	54	38	hamiltonians	hamiltonian	NOUN
ap-4182	54	39	in	in	ADP
ap-4182	54	40	the	the	DET
ap-4182	54	41	case	case	NOUN
ap-4182	54	42	of	of	ADP
ap-4182	54	43	unbroken	unbroken	ADJ
ap-4182	54	44	pt	pt	NOUN
ap-4182	54	45	symmetry	symmetry	NOUN
ap-4182	54	46	.	.	PUNCT
ap-4182	55	1	one	one	NUM
ap-4182	55	2	finds	find	VERB
ap-4182	55	3	the	the	DET
ap-4182	55	4	real	real	ADJ
ap-4182	55	5	part	part	NOUN
ap-4182	55	6	of	of	ADP
ap-4182	55	7	the	the	DET
ap-4182	55	8	complex	complex	ADJ
ap-4182	55	9	berry	berry	NOUN
ap-4182	55	10	phase	phase	NOUN
ap-4182	55	11	to	to	PART
ap-4182	55	12	take	take	VERB
ap-4182	55	13	values	value	NOUN
ap-4182	55	14	0	0	PUNCT
ap-4182	56	1	or	or	CCONJ
ap-4182	56	2	π	π	PROPN
ap-4182	56	3	modulo	modulo	VERB
ap-4182	56	4	2π	2π	NOUN
ap-4182	56	5	.	.	PUNCT
ap-4182	57	1	thus	thus	ADV
ap-4182	57	2	,	,	PUNCT
ap-4182	57	3	a	a	DET
ap-4182	57	4	strict	strict	ADJ
ap-4182	57	5	quantisation	quantisation	NOUN
ap-4182	57	6	is	be	AUX
ap-4182	57	7	still	still	ADV
ap-4182	57	8	present	present	ADJ
ap-4182	57	9	and	and	CCONJ
ap-4182	57	10	the	the	DET
ap-4182	57	11	pt	pt	PROPN
ap-4182	57	12	symmetry	symmetry	NOUN
ap-4182	57	13	protects	protect	VERB
ap-4182	57	14	the	the	DET
ap-4182	57	15	topological	topological	ADJ
ap-4182	57	16	phases	phase	NOUN
ap-4182	57	17	occurring	occur	VERB
ap-4182	57	18	in	in	ADP
ap-4182	57	19	such	such	ADJ
ap-4182	57	20	systems	system	NOUN
ap-4182	57	21	.	.	PUNCT
ap-4182	58	1	3	3	X
ap-4182	58	2	.	.	X
ap-4182	58	3	numerical	numerical	PROPN
ap-4182	58	4	gauge	gauge	NOUN
ap-4182	58	5	smoothing	smooth	VERB
ap-4182	58	6	in	in	ADP
ap-4182	58	7	this	this	DET
ap-4182	58	8	section	section	NOUN
ap-4182	58	9	we	we	PRON
ap-4182	58	10	present	present	VERB
ap-4182	58	11	a	a	DET
ap-4182	58	12	numerical	numerical	ADJ
ap-4182	58	13	procedure	procedure	NOUN
ap-4182	58	14	to	to	PART
ap-4182	58	15	determine	determine	VERB
ap-4182	58	16	the	the	DET
ap-4182	58	17	left	left	ADJ
ap-4182	58	18	and	and	CCONJ
ap-4182	58	19	right	right	ADJ
ap-4182	58	20	eigenvectors	eigenvector	NOUN
ap-4182	58	21	〈	〈	PROPN
ap-4182	58	22	χn|	χn|	PROPN
ap-4182	58	23	and	and	CCONJ
ap-4182	58	24	|φn	|φn	VERB
ap-4182	58	25	〉	〉	NOUN
ap-4182	58	26	in	in	ADP
ap-4182	58	27	an	an	DET
ap-4182	58	28	appropriate	appropriate	ADJ
ap-4182	58	29	smoothed	smoothed	ADJ
ap-4182	58	30	gauge	gauge	NOUN
ap-4182	58	31	to	to	PART
ap-4182	58	32	compute	compute	VERB
ap-4182	58	33	complex	complex	ADJ
ap-4182	58	34	berry	berry	NOUN
ap-4182	58	35	phases	phase	NOUN
ap-4182	58	36	on	on	ADP
ap-4182	58	37	a	a	DET
ap-4182	58	38	discretised	discretised	ADJ
ap-4182	58	39	loop	loop	NOUN
ap-4182	58	40	c	c	NOUN
ap-4182	58	41	=	=	SYM
ap-4182	58	42	(	(	PUNCT
ap-4182	58	43	α1	α1	PROPN
ap-4182	58	44	,	,	PUNCT
ap-4182	58	45	...	...	PUNCT
ap-4182	58	46	,	,	PUNCT
ap-4182	58	47	αj	αj	INTJ
ap-4182	58	48	,	,	PUNCT
ap-4182	58	49	...	...	PUNCT
ap-4182	58	50	,	,	PUNCT
ap-4182	58	51	αm	αm	NOUN
ap-4182	58	52	=	=	SYM
ap-4182	58	53	α1	α1	PROPN
ap-4182	58	54	)	)	PUNCT
ap-4182	58	55	in	in	ADP
ap-4182	58	56	parameter	parameter	NOUN
ap-4182	58	57	space	space	NOUN
ap-4182	58	58	.	.	PUNCT
ap-4182	59	1	this	this	PRON
ap-4182	59	2	is	be	AUX
ap-4182	59	3	necessary	necessary	ADJ
ap-4182	59	4	for	for	ADP
ap-4182	59	5	the	the	DET
ap-4182	59	6	evaluation	evaluation	NOUN
ap-4182	59	7	of	of	ADP
ap-4182	59	8	integrals	integral	NOUN
ap-4182	59	9	of	of	ADP
ap-4182	59	10	the	the	DET
ap-4182	59	11	form	form	NOUN
ap-4182	59	12	in	in	ADP
ap-4182	59	13	(	(	PUNCT
ap-4182	59	14	2	2	NUM
ap-4182	59	15	)	)	PUNCT
ap-4182	59	16	.	.	PUNCT
ap-4182	60	1	typically	typically	ADV
ap-4182	60	2	the	the	DET
ap-4182	60	3	left	left	ADJ
ap-4182	60	4	and	and	CCONJ
ap-4182	60	5	right	right	ADJ
ap-4182	60	6	eigenvectors	eigenvector	NOUN
ap-4182	60	7	have	have	VERB
ap-4182	60	8	to	to	PART
ap-4182	60	9	be	be	AUX
ap-4182	60	10	calculated	calculate	VERB
ap-4182	60	11	independently	independently	ADV
ap-4182	60	12	,	,	PUNCT
ap-4182	60	13	and	and	CCONJ
ap-4182	60	14	each	each	PRON
ap-4182	60	15	of	of	ADP
ap-4182	60	16	them	they	PRON
ap-4182	60	17	has	have	VERB
ap-4182	60	18	an	an	DET
ap-4182	60	19	arbitrary	arbitrary	ADJ
ap-4182	60	20	global	global	ADJ
ap-4182	60	21	phase	phase	NOUN
ap-4182	60	22	.	.	PUNCT
ap-4182	61	1	the	the	DET
ap-4182	61	2	biorthogonal	biorthogonal	ADJ
ap-4182	61	3	normalisation	normalisation	NOUN
ap-4182	61	4	condition	condition	NOUN
ap-4182	61	5	[	[	X
ap-4182	61	6	39	39	NUM
ap-4182	61	7	]	]	PUNCT
ap-4182	61	8	,	,	PUNCT
ap-4182	61	9	〈	〈	PROPN
ap-4182	61	10	χn(αj)|	χn(αj)|	PRON
ap-4182	61	11	→	→	PUNCT
ap-4182	61	12	〈	〈	PROPN
ap-4182	61	13	χn(αj)|√	χn(αj)|√	NOUN
ap-4182	61	14	〈	〈	NOUN
ap-4182	61	15	χn(αj)|φn(αj	χn(αj)|φn(αj	PROPN
ap-4182	61	16	)	)	PUNCT
ap-4182	61	17	〉	〉	PROPN
ap-4182	61	18	,	,	PUNCT
ap-4182	61	19	(	(	PUNCT
ap-4182	61	20	4a	4a	NUM
ap-4182	61	21	)	)	PUNCT
ap-4182	61	22	|φn(αj	|φn(αj	PROPN
ap-4182	61	23	)	)	PUNCT
ap-4182	61	24	〉	〉	PROPN
ap-4182	61	25	→	→	SYM
ap-4182	61	26	|φn(αj)〉√	|φn(αj)〉√	PROPN
ap-4182	61	27	〈	〈	PROPN
ap-4182	61	28	χn(αj)|φn(αj	χn(αj)|φn(αj	NOUN
ap-4182	61	29	)	)	PUNCT
ap-4182	61	30	〉	〉	PROPN
ap-4182	61	31	,	,	PUNCT
ap-4182	61	32	(	(	PUNCT
ap-4182	61	33	4b	4b	X
ap-4182	61	34	)	)	PUNCT
ap-4182	61	35	chooses	choose	VERB
ap-4182	61	36	one	one	NUM
ap-4182	61	37	arbitrary	arbitrary	ADJ
ap-4182	61	38	global	global	ADJ
ap-4182	61	39	phase	phase	NOUN
ap-4182	61	40	for	for	ADP
ap-4182	61	41	each	each	DET
ap-4182	61	42	αj	αj	NOUN
ap-4182	61	43	.	.	PUNCT
ap-4182	62	1	this	this	PRON
ap-4182	62	2	is	be	AUX
ap-4182	62	3	sufficient	sufficient	ADJ
ap-4182	62	4	if	if	SCONJ
ap-4182	62	5	only	only	ADV
ap-4182	62	6	products	product	NOUN
ap-4182	62	7	or	or	CCONJ
ap-4182	62	8	matrix	matrix	NOUN
ap-4182	62	9	elements	element	NOUN
ap-4182	62	10	of	of	ADP
ap-4182	62	11	eigenstates	eigenstate	NOUN
ap-4182	62	12	belonging	belong	VERB
ap-4182	62	13	to	to	ADP
ap-4182	62	14	the	the	DET
ap-4182	62	15	same	same	ADJ
ap-4182	62	16	point	point	NOUN
ap-4182	62	17	in	in	ADP
ap-4182	62	18	parameter	parameter	NOUN
ap-4182	62	19	space	space	NOUN
ap-4182	62	20	are	be	AUX
ap-4182	62	21	required	require	VERB
ap-4182	62	22	.	.	PUNCT
ap-4182	63	1	however	however	ADV
ap-4182	63	2	,	,	PUNCT
ap-4182	63	3	for	for	ADP
ap-4182	63	4	numerical	numerical	ADJ
ap-4182	63	5	derivatives	derivative	NOUN
ap-4182	63	6	used	use	VERB
ap-4182	63	7	in	in	ADP
ap-4182	63	8	(	(	PUNCT
ap-4182	63	9	2	2	X
ap-4182	63	10	)	)	PUNCT
ap-4182	63	11	the	the	DET
ap-4182	63	12	remaining	remain	VERB
ap-4182	63	13	global	global	ADJ
ap-4182	63	14	phases	phase	NOUN
ap-4182	63	15	of	of	ADP
ap-4182	63	16	successive	successive	ADJ
ap-4182	63	17	steps	step	NOUN
ap-4182	63	18	in	in	ADP
ap-4182	63	19	αj	αj	NOUN
ap-4182	63	20	along	along	ADP
ap-4182	63	21	the	the	DET
ap-4182	63	22	loop	loop	NOUN
ap-4182	63	23	c	c	PROPN
ap-4182	63	24	can	can	AUX
ap-4182	63	25	spoil	spoil	VERB
ap-4182	63	26	the	the	DET
ap-4182	63	27	complex	complex	ADJ
ap-4182	63	28	zak	zak	PROPN
ap-4182	63	29	phase	phase	NOUN
ap-4182	63	30	.	.	PUNCT
ap-4182	64	1	a	a	DET
ap-4182	64	2	fixation	fixation	NOUN
ap-4182	64	3	of	of	ADP
ap-4182	64	4	the	the	DET
ap-4182	64	5	phase	phase	NOUN
ap-4182	64	6	between	between	ADP
ap-4182	64	7	consecutive	consecutive	ADJ
ap-4182	64	8	steps	step	NOUN
ap-4182	64	9	that	that	PRON
ap-4182	64	10	does	do	AUX
ap-4182	64	11	not	not	PART
ap-4182	64	12	distort	distort	VERB
ap-4182	64	13	the	the	DET
ap-4182	64	14	desired	desire	VERB
ap-4182	64	15	result	result	NOUN
ap-4182	64	16	is	be	AUX
ap-4182	64	17	required	require	VERB
ap-4182	64	18	.	.	PUNCT
ap-4182	65	1	starting	start	VERB
ap-4182	65	2	point	point	NOUN
ap-4182	65	3	for	for	ADP
ap-4182	65	4	the	the	DET
ap-4182	65	5	gauge	gauge	NOUN
ap-4182	65	6	smoothing	smoothing	NOUN
ap-4182	65	7	procedure	procedure	NOUN
ap-4182	65	8	are	be	AUX
ap-4182	65	9	the	the	DET
ap-4182	65	10	left	left	ADJ
ap-4182	65	11	and	and	CCONJ
ap-4182	65	12	right	right	ADJ
ap-4182	65	13	handed	handed	ADJ
ap-4182	65	14	versions	version	NOUN
ap-4182	65	15	of	of	ADP
ap-4182	65	16	the	the	DET
ap-4182	65	17	timeindependent	timeindependent	NOUN
ap-4182	65	18	schrödinger	schrödinger	ADJ
ap-4182	65	19	equation	equation	NOUN
ap-4182	65	20	,	,	PUNCT
ap-4182	65	21	〈	〈	PROPN
ap-4182	65	22	χn(α)|h(α	χn(α)|h(α	X
ap-4182	65	23	)	)	PUNCT
ap-4182	65	24	=	=	SYM
ap-4182	65	25	en(α	en(α	NOUN
ap-4182	65	26	)	)	PUNCT
ap-4182	66	1	〈	〈	NOUN
ap-4182	66	2	χn(α)|	χn(α)|	NOUN
ap-4182	66	3	,	,	PUNCT
ap-4182	66	4	(	(	PUNCT
ap-4182	66	5	5a	5a	NUM
ap-4182	66	6	)	)	PUNCT
ap-4182	66	7	h(α	h(α	ADJ
ap-4182	66	8	)	)	PUNCT
ap-4182	66	9	|φn(α	|φn(α	NUM
ap-4182	66	10	)	)	PUNCT
ap-4182	66	11	〉	〉	NOUN
ap-4182	66	12	=	=	SYM
ap-4182	66	13	en(α	en(α	NOUN
ap-4182	66	14	)	)	PUNCT
ap-4182	66	15	|φn(α	|φn(α	NUM
ap-4182	66	16	)	)	PUNCT
ap-4182	66	17	〉	〉	PROPN
ap-4182	66	18	,	,	PUNCT
ap-4182	66	19	(	(	PUNCT
ap-4182	66	20	5b	5b	NUM
ap-4182	66	21	)	)	PUNCT
ap-4182	66	22	defining	define	VERB
ap-4182	66	23	a	a	DET
ap-4182	66	24	set	set	NOUN
ap-4182	66	25	of	of	ADP
ap-4182	66	26	natural	natural	ADJ
ap-4182	66	27	left	left	ADJ
ap-4182	66	28	and	and	CCONJ
ap-4182	66	29	right	right	ADJ
ap-4182	66	30	basis	basis	NOUN
ap-4182	66	31	states	state	NOUN
ap-4182	66	32	〈	〈	PROPN
ap-4182	66	33	χn(α)|	χn(α)|	NOUN
ap-4182	66	34	and	and	CCONJ
ap-4182	66	35	|φn(α	|φn(α	NUM
ap-4182	66	36	)	)	PUNCT
ap-4182	66	37	〉	〉	PROPN
ap-4182	66	38	.	.	PUNCT
ap-4182	67	1	these	these	DET
ap-4182	67	2	equations	equation	NOUN
ap-4182	67	3	are	be	AUX
ap-4182	67	4	solved	solve	VERB
ap-4182	67	5	for	for	ADP
ap-4182	67	6	every	every	DET
ap-4182	67	7	point	point	NOUN
ap-4182	67	8	αj	αj	NOUN
ap-4182	67	9	of	of	ADP
ap-4182	67	10	the	the	DET
ap-4182	67	11	discretised	discretise	VERB
ap-4182	67	12	loop	loop	NOUN
ap-4182	67	13	c	c	PROPN
ap-4182	67	14	in	in	ADP
ap-4182	67	15	parameter	parameter	NOUN
ap-4182	67	16	space	space	NOUN
ap-4182	67	17	providing	provide	VERB
ap-4182	67	18	the	the	DET
ap-4182	67	19	eigenvalues	eigenvalue	NOUN
ap-4182	67	20	en(αj	en(αj	NOUN
ap-4182	67	21	)	)	PUNCT
ap-4182	67	22	and	and	CCONJ
ap-4182	67	23	the	the	DET
ap-4182	67	24	unnormalised	unnormalised	ADJ
ap-4182	67	25	states	state	NOUN
ap-4182	67	26	of	of	ADP
ap-4182	67	27	a	a	DET
ap-4182	67	28	biorthogonal	biorthogonal	ADJ
ap-4182	67	29	basis	basis	NOUN
ap-4182	67	30	{	{	PUNCT
ap-4182	67	31	〈	〈	PROPN
ap-4182	67	32	χn(αj)|	χn(αj)|	ADJ
ap-4182	67	33	,	,	PUNCT
ap-4182	67	34	|φn(αj	|φn(αj	PROPN
ap-4182	67	35	)	)	PUNCT
ap-4182	67	36	〉	〉	NOUN
ap-4182	67	37	}	}	PUNCT
ap-4182	67	38	of	of	ADP
ap-4182	67	39	the	the	DET
ap-4182	67	40	hamiltonian	hamiltonian	ADJ
ap-4182	67	41	h(αj	h(αj	PROPN
ap-4182	67	42	)	)	PUNCT
ap-4182	67	43	at	at	ADP
ap-4182	67	44	each	each	DET
ap-4182	67	45	point	point	NOUN
ap-4182	67	46	αj	αj	NOUN
ap-4182	67	47	.	.	PUNCT
ap-4182	68	1	here	here	ADV
ap-4182	68	2	the	the	DET
ap-4182	68	3	basis	basis	NOUN
ap-4182	68	4	states	state	NOUN
ap-4182	68	5	are	be	AUX
ap-4182	68	6	determined	determine	VERB
ap-4182	68	7	up	up	ADP
ap-4182	68	8	to	to	ADP
ap-4182	68	9	the	the	DET
ap-4182	68	10	aforementioned	aforementioned	ADJ
ap-4182	68	11	arbitrary	arbitrary	ADJ
ap-4182	68	12	phases	phase	NOUN
ap-4182	68	13	.	.	PUNCT
ap-4182	69	1	to	to	PART
ap-4182	69	2	smooth	smooth	VERB
ap-4182	69	3	the	the	DET
ap-4182	69	4	gauge	gauge	NOUN
ap-4182	69	5	within	within	ADP
ap-4182	69	6	the	the	DET
ap-4182	69	7	loop	loop	NOUN
ap-4182	69	8	in	in	ADP
ap-4182	69	9	parameter	parameter	NOUN
ap-4182	69	10	space	space	NOUN
ap-4182	69	11	with	with	ADP
ap-4182	69	12	basepoint	basepoint	PROPN
ap-4182	69	13	α1	α1	PROPN
ap-4182	69	14	one	one	PRON
ap-4182	69	15	chooses	choose	VERB
ap-4182	69	16	an	an	DET
ap-4182	69	17	arbitrary	arbitrary	ADJ
ap-4182	69	18	global	global	ADJ
ap-4182	69	19	phase	phase	NOUN
ap-4182	69	20	.	.	PUNCT
ap-4182	70	1	it	it	PRON
ap-4182	70	2	is	be	AUX
ap-4182	70	3	most	most	ADV
ap-4182	70	4	convenient	convenient	ADJ
ap-4182	70	5	to	to	PART
ap-4182	70	6	do	do	VERB
ap-4182	70	7	this	this	PRON
ap-4182	70	8	for	for	ADP
ap-4182	70	9	the	the	DET
ap-4182	70	10	basepoint	basepoint	PROPN
ap-4182	70	11	.	.	PUNCT
ap-4182	71	1	the	the	DET
ap-4182	71	2	corresponding	corresponding	ADJ
ap-4182	71	3	eigenstates	eigenstate	NOUN
ap-4182	71	4	are	be	AUX
ap-4182	71	5	normalised	normalise	VERB
ap-4182	71	6	according	accord	VERB
ap-4182	71	7	to	to	ADP
ap-4182	71	8	the	the	DET
ap-4182	71	9	conditions	condition	NOUN
ap-4182	71	10	(	(	PUNCT
ap-4182	71	11	4a	4a	NUM
ap-4182	71	12	)	)	PUNCT
ap-4182	71	13	and	and	CCONJ
ap-4182	71	14	(	(	PUNCT
ap-4182	71	15	4b	4b	PROPN
ap-4182	71	16	)	)	PUNCT
ap-4182	71	17	.	.	PUNCT
ap-4182	72	1	the	the	DET
ap-4182	72	2	following	follow	VERB
ap-4182	72	3	two	two	NUM
ap-4182	72	4	-	-	PUNCT
ap-4182	72	5	stage	stage	NOUN
ap-4182	72	6	procedure	procedure	NOUN
ap-4182	72	7	transfers	transfer	VERB
ap-4182	72	8	the	the	DET
ap-4182	72	9	choice	choice	NOUN
ap-4182	72	10	of	of	ADP
ap-4182	72	11	the	the	DET
ap-4182	72	12	global	global	ADJ
ap-4182	72	13	phase	phase	NOUN
ap-4182	72	14	at	at	ADP
ap-4182	72	15	α1	α1	PROPN
ap-4182	72	16	onto	onto	ADP
ap-4182	72	17	the	the	DET
ap-4182	72	18	other	other	ADJ
ap-4182	72	19	basis	basis	NOUN
ap-4182	72	20	states	state	NOUN
ap-4182	72	21	along	along	ADP
ap-4182	72	22	the	the	DET
ap-4182	72	23	loop	loop	NOUN
ap-4182	72	24	c.	c.	PROPN
ap-4182	72	25	first	first	ADJ
ap-4182	72	26	one	one	NUM
ap-4182	72	27	modifies	modify	VERB
ap-4182	72	28	the	the	DET
ap-4182	72	29	phases	phase	NOUN
ap-4182	72	30	of	of	ADP
ap-4182	72	31	the	the	DET
ap-4182	72	32	states	state	NOUN
ap-4182	72	33	〈	〈	PROPN
ap-4182	72	34	χn(αj)|	χn(αj)|	PUNCT
ap-4182	72	35	and	and	CCONJ
ap-4182	72	36	|φn(αj	|φn(αj	PROPN
ap-4182	72	37	)	)	PUNCT
ap-4182	72	38	〉	〉	NOUN
ap-4182	72	39	iteratively	iteratively	ADV
ap-4182	72	40	by	by	ADP
ap-4182	72	41	〈	〈	PROPN
ap-4182	72	42	χn(αj)|	χn(αj)|	PROPN
ap-4182	72	43	→	→	SYM
ap-4182	72	44	〈	〈	PROPN
ap-4182	72	45	χn(αj)|	χn(αj)|	ADJ
ap-4182	72	46	e−i	e−i	NOUN
ap-4182	72	47	arg(〈χn(αj)|φn(αj−1	arg(〈χn(αj)|φn(αj−1	NOUN
ap-4182	72	48	)	)	PUNCT
ap-4182	72	49	〉	〉	NOUN
ap-4182	72	50	)	)	PUNCT
ap-4182	72	51	,	,	PUNCT
ap-4182	72	52	(	(	PUNCT
ap-4182	72	53	6a	6a	NOUN
ap-4182	72	54	)	)	PUNCT
ap-4182	72	55	|φn(αj	|φn(αj	NOUN
ap-4182	72	56	)	)	PUNCT
ap-4182	72	57	〉	〉	PROPN
ap-4182	72	58	→	→	SYM
ap-4182	72	59	|φn(αj	|φn(αj	NOUN
ap-4182	72	60	)	)	PUNCT
ap-4182	72	61	〉	〉	PROPN
ap-4182	72	62	e−i	e−i	NOUN
ap-4182	72	63	arg(〈χn(αj−1)|φn(αj	arg(〈χn(αj−1)|φn(αj	NOUN
ap-4182	72	64	)	)	PUNCT
ap-4182	72	65	〉	〉	NOUN
ap-4182	72	66	)	)	PUNCT
ap-4182	72	67	(	(	PUNCT
ap-4182	72	68	6b	6b	NOUN
ap-4182	72	69	)	)	PUNCT
ap-4182	72	70	followed	follow	VERB
ap-4182	72	71	by	by	ADP
ap-4182	72	72	a	a	DET
ap-4182	72	73	normalisation	normalisation	NOUN
ap-4182	72	74	of	of	ADP
ap-4182	72	75	the	the	DET
ap-4182	72	76	states	state	NOUN
ap-4182	72	77	according	accord	VERB
ap-4182	72	78	to	to	ADP
ap-4182	72	79	(	(	PUNCT
ap-4182	72	80	4a	4a	NUM
ap-4182	72	81	)	)	PUNCT
ap-4182	72	82	and	and	CCONJ
ap-4182	72	83	(	(	PUNCT
ap-4182	72	84	4b	4b	PROPN
ap-4182	72	85	)	)	PUNCT
ap-4182	72	86	.	.	PUNCT
ap-4182	73	1	equations	equation	NOUN
ap-4182	73	2	(	(	PUNCT
ap-4182	73	3	6a	6a	NOUN
ap-4182	73	4	)	)	PUNCT
ap-4182	73	5	and	and	CCONJ
ap-4182	73	6	(	(	PUNCT
ap-4182	73	7	6b	6b	NOUN
ap-4182	73	8	)	)	PUNCT
ap-4182	73	9	relate	relate	VERB
ap-4182	73	10	the	the	DET
ap-4182	73	11	vectors	vector	NOUN
ap-4182	73	12	of	of	ADP
ap-4182	73	13	step	step	NOUN
ap-4182	73	14	j	j	PROPN
ap-4182	73	15	to	to	ADP
ap-4182	73	16	those	those	PRON
ap-4182	73	17	of	of	ADP
ap-4182	73	18	step	step	NOUN
ap-4182	73	19	j	j	PROPN
ap-4182	73	20	−	−	PROPN
ap-4182	73	21	1	1	NUM
ap-4182	73	22	by	by	ADP
ap-4182	73	23	ensuring	ensure	VERB
ap-4182	73	24	i	i	PRON
ap-4182	73	25	m	m	VERB
ap-4182	73	26	(	(	PUNCT
ap-4182	73	27	〈	〈	PROPN
ap-4182	73	28	χn(αj)|φn(αj−1	χn(αj)|φn(αj−1	PROPN
ap-4182	73	29	)	)	PUNCT
ap-4182	73	30	〉	〉	NOUN
ap-4182	73	31	)	)	PUNCT
ap-4182	74	1	=	=	SYM
ap-4182	74	2	0	0	NUM
ap-4182	74	3	,	,	PUNCT
ap-4182	74	4	(	(	PUNCT
ap-4182	74	5	7a	7a	X
ap-4182	74	6	)	)	PUNCT
ap-4182	74	7	i	i	PRON
ap-4182	74	8	m	m	VERB
ap-4182	74	9	(	(	PUNCT
ap-4182	74	10	〈	〈	PROPN
ap-4182	74	11	χn(αj−1)|φn(αj	χn(αj−1)|φn(αj	NOUN
ap-4182	74	12	)	)	PUNCT
ap-4182	74	13	〉	〉	NOUN
ap-4182	74	14	)	)	PUNCT
ap-4182	75	1	=	=	SYM
ap-4182	75	2	0	0	NUM
ap-4182	75	3	,	,	PUNCT
ap-4182	75	4	(	(	PUNCT
ap-4182	75	5	7b	7b	NOUN
ap-4182	75	6	)	)	PUNCT
ap-4182	75	7	471	471	NUM
ap-4182	75	8	m.	m.	PROPN
ap-4182	75	9	wagner	wagner	PROPN
ap-4182	75	10	,	,	PUNCT
ap-4182	75	11	f.	f.	PROPN
ap-4182	75	12	dangel	dangel	PROPN
ap-4182	75	13	,	,	PUNCT
ap-4182	75	14	h.	h.	PROPN
ap-4182	75	15	cartarius	cartarius	PROPN
ap-4182	75	16	et	et	PROPN
ap-4182	75	17	al	al	PROPN
ap-4182	75	18	.	.	PROPN
ap-4182	76	1	acta	acta	PROPN
ap-4182	76	2	polytechnica	polytechnica	PROPN
ap-4182	76	3	which	which	PRON
ap-4182	76	4	is	be	AUX
ap-4182	76	5	a	a	DET
ap-4182	76	6	valid	valid	ADJ
ap-4182	76	7	condition	condition	NOUN
ap-4182	76	8	in	in	ADP
ap-4182	76	9	the	the	DET
ap-4182	76	10	continuous	continuous	ADJ
ap-4182	76	11	limit	limit	NOUN
ap-4182	76	12	.	.	PUNCT
ap-4182	77	1	the	the	DET
ap-4182	77	2	normalisation	normalisation	NOUN
ap-4182	77	3	conditions	condition	NOUN
ap-4182	77	4	(	(	PUNCT
ap-4182	77	5	4a	4a	NUM
ap-4182	77	6	)	)	PUNCT
ap-4182	77	7	and	and	CCONJ
ap-4182	77	8	(	(	PUNCT
ap-4182	77	9	4b	4b	X
ap-4182	77	10	)	)	PUNCT
ap-4182	77	11	ensure	ensure	VERB
ap-4182	77	12	that	that	SCONJ
ap-4182	77	13	the	the	DET
ap-4182	77	14	basis	basis	NOUN
ap-4182	77	15	states	state	NOUN
ap-4182	77	16	now	now	ADV
ap-4182	77	17	fulfil	fulfil	VERB
ap-4182	77	18	〈	〈	NOUN
ap-4182	77	19	χm(αj)|φn(αj	χm(αj)|φn(αj	NOUN
ap-4182	77	20	)	)	PUNCT
ap-4182	77	21	〉	〉	NOUN
ap-4182	77	22	=	=	SYM
ap-4182	77	23	δmn	δmn	NOUN
ap-4182	77	24	(	(	PUNCT
ap-4182	77	25	8)	8)	NUM
ap-4182	77	26	for	for	ADP
ap-4182	77	27	j	j	PROPN
ap-4182	77	28	∈	∈	PROPN
ap-4182	77	29	{	{	PUNCT
ap-4182	77	30	1	1	NUM
ap-4182	77	31	,	,	PUNCT
ap-4182	77	32	.	.	PUNCT
ap-4182	77	33	.	.	PUNCT
ap-4182	77	34	.	.	PUNCT
ap-4182	78	1	,	,	PUNCT
ap-4182	78	2	m	m	VERB
ap-4182	78	3	}	}	PUNCT
ap-4182	78	4	and	and	CCONJ
ap-4182	78	5	for	for	ADP
ap-4182	78	6	all	all	DET
ap-4182	78	7	n	n	NOUN
ap-4182	78	8	and	and	CCONJ
ap-4182	78	9	m.	m.	NOUN
ap-4182	78	10	as	as	ADP
ap-4182	78	11	a	a	DET
ap-4182	78	12	result	result	NOUN
ap-4182	78	13	of	of	ADP
ap-4182	78	14	the	the	DET
ap-4182	78	15	first	first	ADJ
ap-4182	78	16	step	step	NOUN
ap-4182	78	17	the	the	DET
ap-4182	78	18	arbitrary	arbitrary	ADJ
ap-4182	78	19	global	global	ADJ
ap-4182	78	20	phases	phase	NOUN
ap-4182	78	21	have	have	AUX
ap-4182	78	22	been	be	AUX
ap-4182	78	23	removed	remove	VERB
ap-4182	78	24	.	.	PUNCT
ap-4182	79	1	only	only	ADV
ap-4182	79	2	one	one	NUM
ap-4182	79	3	arbitrary	arbitrary	ADJ
ap-4182	79	4	phase	phase	NOUN
ap-4182	79	5	is	be	AUX
ap-4182	79	6	left	leave	VERB
ap-4182	79	7	,	,	PUNCT
ap-4182	79	8	which	which	PRON
ap-4182	79	9	has	have	VERB
ap-4182	79	10	no	no	DET
ap-4182	79	11	influence	influence	NOUN
ap-4182	79	12	,	,	PUNCT
ap-4182	79	13	since	since	SCONJ
ap-4182	79	14	it	it	PRON
ap-4182	79	15	is	be	AUX
ap-4182	79	16	identical	identical	ADJ
ap-4182	79	17	for	for	ADP
ap-4182	79	18	all	all	DET
ap-4182	79	19	right	right	ADJ
ap-4182	79	20	eigenvectors	eigenvector	NOUN
ap-4182	79	21	and	and	CCONJ
ap-4182	79	22	its	its	PRON
ap-4182	79	23	complex	complex	ADJ
ap-4182	79	24	conjugate	conjugate	NOUN
ap-4182	79	25	for	for	ADP
ap-4182	79	26	all	all	DET
ap-4182	79	27	left	leave	VERB
ap-4182	79	28	eigenvectors	eigenvector	NOUN
ap-4182	79	29	.	.	PUNCT
ap-4182	80	1	however	however	ADV
ap-4182	80	2	,	,	PUNCT
ap-4182	80	3	the	the	DET
ap-4182	80	4	biorthogonal	biorthogonal	ADJ
ap-4182	80	5	basis	basis	NOUN
ap-4182	80	6	following	follow	VERB
ap-4182	80	7	from	from	ADP
ap-4182	80	8	the	the	DET
ap-4182	80	9	procedure	procedure	NOUN
ap-4182	80	10	so	so	ADV
ap-4182	80	11	far	far	ADV
ap-4182	80	12	is	be	AUX
ap-4182	80	13	not	not	PART
ap-4182	80	14	singlevalued	singlevalue	VERB
ap-4182	80	15	in	in	ADP
ap-4182	80	16	the	the	DET
ap-4182	80	17	parameter	parameter	NOUN
ap-4182	80	18	space	space	NOUN
ap-4182	80	19	.	.	PUNCT
ap-4182	81	1	in	in	ADP
ap-4182	81	2	particular	particular	ADJ
ap-4182	81	3	,	,	PUNCT
ap-4182	81	4	the	the	DET
ap-4182	81	5	vectors	vector	NOUN
ap-4182	81	6	at	at	ADP
ap-4182	81	7	the	the	DET
ap-4182	81	8	starting	starting	NOUN
ap-4182	81	9	and	and	CCONJ
ap-4182	81	10	end	end	VERB
ap-4182	81	11	point	point	NOUN
ap-4182	81	12	of	of	ADP
ap-4182	81	13	the	the	DET
ap-4182	81	14	loop	loop	NOUN
ap-4182	81	15	are	be	AUX
ap-4182	81	16	not	not	PART
ap-4182	81	17	identical	identical	ADJ
ap-4182	81	18	.	.	PUNCT
ap-4182	82	1	for	for	ADP
ap-4182	82	2	the	the	DET
ap-4182	82	3	calculation	calculation	NOUN
ap-4182	82	4	of	of	ADP
ap-4182	82	5	a	a	DET
ap-4182	82	6	berry	berry	NOUN
ap-4182	82	7	phase	phase	NOUN
ap-4182	82	8	a	a	DET
ap-4182	82	9	continuous	continuous	ADJ
ap-4182	82	10	single	single	ADV
ap-4182	82	11	-	-	PUNCT
ap-4182	82	12	valued	value	VERB
ap-4182	82	13	phase	phase	NOUN
ap-4182	82	14	function	function	NOUN
ap-4182	82	15	is	be	AUX
ap-4182	82	16	essential	essential	ADJ
ap-4182	82	17	[	[	X
ap-4182	82	18	42	42	NUM
ap-4182	82	19	]	]	PUNCT
ap-4182	82	20	,	,	PUNCT
ap-4182	82	21	and	and	CCONJ
ap-4182	82	22	thus	thus	ADV
ap-4182	82	23	has	have	VERB
ap-4182	82	24	to	to	PART
ap-4182	82	25	be	be	AUX
ap-4182	82	26	established	establish	VERB
ap-4182	82	27	.	.	PUNCT
ap-4182	83	1	to	to	ADP
ap-4182	83	2	this	this	DET
ap-4182	83	3	end	end	NOUN
ap-4182	83	4	in	in	ADP
ap-4182	83	5	the	the	DET
ap-4182	83	6	second	second	ADJ
ap-4182	83	7	step	step	NOUN
ap-4182	83	8	one	one	NUM
ap-4182	83	9	adjusts	adjust	VERB
ap-4182	83	10	the	the	DET
ap-4182	83	11	basis	basis	NOUN
ap-4182	83	12	states	state	NOUN
ap-4182	83	13	such	such	ADJ
ap-4182	83	14	that	that	SCONJ
ap-4182	83	15	they	they	PRON
ap-4182	83	16	are	be	AUX
ap-4182	83	17	the	the	DET
ap-4182	83	18	same	same	ADJ
ap-4182	83	19	at	at	ADP
ap-4182	83	20	the	the	DET
ap-4182	83	21	starting	starting	NOUN
ap-4182	83	22	and	and	CCONJ
ap-4182	83	23	the	the	DET
ap-4182	83	24	end	end	NOUN
ap-4182	83	25	point	point	NOUN
ap-4182	83	26	of	of	ADP
ap-4182	83	27	the	the	DET
ap-4182	83	28	loop	loop	NOUN
ap-4182	83	29	.	.	PUNCT
ap-4182	84	1	this	this	PRON
ap-4182	84	2	can	can	AUX
ap-4182	84	3	be	be	AUX
ap-4182	84	4	achieved	achieve	VERB
ap-4182	84	5	by	by	ADP
ap-4182	84	6	compensating	compensate	VERB
ap-4182	84	7	the	the	DET
ap-4182	84	8	phase	phase	NOUN
ap-4182	84	9	difference	difference	NOUN
ap-4182	84	10	between	between	ADP
ap-4182	84	11	the	the	DET
ap-4182	84	12	states	state	NOUN
ap-4182	84	13	at	at	ADP
ap-4182	84	14	the	the	DET
ap-4182	84	15	basepoint	basepoint	NOUN
ap-4182	84	16	,	,	PUNCT
ap-4182	84	17	〈	〈	PROPN
ap-4182	84	18	χn(α1)|	χn(α1)|	PROPN
ap-4182	84	19	and	and	CCONJ
ap-4182	84	20	〈	〈	PROPN
ap-4182	84	21	χn(αm	χn(αm	PROPN
ap-4182	84	22	)	)	PUNCT
ap-4182	85	1	|	|	ADV
ap-4182	85	2	,	,	PUNCT
ap-4182	85	3	respectively	respectively	ADV
ap-4182	85	4	,	,	PUNCT
ap-4182	85	5	as	as	ADV
ap-4182	85	6	well	well	ADV
ap-4182	85	7	as	as	ADP
ap-4182	85	8	|φn(α1	|φn(α1	NOUN
ap-4182	85	9	)	)	PUNCT
ap-4182	85	10	〉	〉	NOUN
ap-4182	85	11	and	and	CCONJ
ap-4182	85	12	|φn(αm	|φn(αm	NOUN
ap-4182	85	13	)	)	PUNCT
ap-4182	85	14	〉	〉	NOUN
ap-4182	85	15	.	.	PUNCT
ap-4182	86	1	this	this	PRON
ap-4182	86	2	remains	remain	VERB
ap-4182	86	3	true	true	ADJ
ap-4182	86	4	for	for	ADP
ap-4182	86	5	single	single	ADJ
ap-4182	86	6	vector	vector	NOUN
ap-4182	86	7	components	component	NOUN
ap-4182	86	8	.	.	PUNCT
ap-4182	87	1	therefore	therefore	ADV
ap-4182	87	2	we	we	PRON
ap-4182	87	3	calculate	calculate	VERB
ap-4182	87	4	the	the	DET
ap-4182	87	5	phase	phase	NOUN
ap-4182	87	6	difference	difference	NOUN
ap-4182	87	7	of	of	ADP
ap-4182	87	8	the	the	DET
ap-4182	87	9	first	first	ADJ
ap-4182	87	10	non	non	ADJ
ap-4182	87	11	-	-	ADJ
ap-4182	87	12	vanishing	vanishing	ADJ
ap-4182	87	13	component	component	NOUN
ap-4182	87	14	p	p	NOUN
ap-4182	87	15	of	of	ADP
ap-4182	87	16	the	the	DET
ap-4182	87	17	left	left	ADJ
ap-4182	87	18	basis	basis	NOUN
ap-4182	87	19	states	state	NOUN
ap-4182	87	20	〈	〈	PROPN
ap-4182	87	21	χn(α1)|	χn(α1)|	PROPN
ap-4182	87	22	and	and	CCONJ
ap-4182	87	23	〈	〈	PROPN
ap-4182	87	24	χn(αm	χn(αm	PROPN
ap-4182	87	25	)	)	PUNCT
ap-4182	87	26	|	|	ADV
ap-4182	87	27	,	,	PUNCT
ap-4182	87	28	∆ϕn	∆ϕn	X
ap-4182	87	29	=	=	PUNCT
ap-4182	87	30	ϕn	ϕn	PROPN
ap-4182	87	31	,	,	PUNCT
ap-4182	87	32	m	m	VERB
ap-4182	87	33	−	−	PROPN
ap-4182	87	34	ϕn,1	ϕn,1	PROPN
ap-4182	87	35	+	+	CCONJ
ap-4182	87	36	2πxn	2πxn	NUM
ap-4182	87	37	,	,	PUNCT
ap-4182	87	38	(	(	PUNCT
ap-4182	87	39	9	9	NUM
ap-4182	87	40	)	)	PUNCT
ap-4182	87	41	where	where	SCONJ
ap-4182	87	42	ϕn	ϕn	INTJ
ap-4182	87	43	,	,	PUNCT
ap-4182	87	44	j	j	PROPN
ap-4182	87	45	=	=	PUNCT
ap-4182	87	46	arg	arg	NOUN
ap-4182	87	47	(	(	PUNCT
ap-4182	87	48	〈	〈	PROPN
ap-4182	87	49	χn(αj)|p	χn(αj)|p	PRON
ap-4182	87	50	)	)	PUNCT
ap-4182	87	51	is	be	AUX
ap-4182	87	52	the	the	DET
ap-4182	87	53	argument	argument	NOUN
ap-4182	87	54	of	of	ADP
ap-4182	87	55	component	component	NOUN
ap-4182	87	56	p	p	NOUN
ap-4182	87	57	of	of	ADP
ap-4182	87	58	the	the	DET
ap-4182	87	59	left	left	ADJ
ap-4182	87	60	eigenvector	eigenvector	NOUN
ap-4182	87	61	at	at	ADP
ap-4182	87	62	the	the	DET
ap-4182	87	63	point	point	NOUN
ap-4182	87	64	αj	αj	NOUN
ap-4182	87	65	in	in	ADP
ap-4182	87	66	parameter	parameter	NOUN
ap-4182	87	67	space	space	NOUN
ap-4182	87	68	and	and	CCONJ
ap-4182	87	69	x	x	NOUN
ap-4182	87	70	denotes	denote	VERB
ap-4182	87	71	the	the	DET
ap-4182	87	72	sum	sum	NOUN
ap-4182	87	73	of	of	ADP
ap-4182	87	74	directed	direct	VERB
ap-4182	87	75	crossings	crossing	NOUN
ap-4182	87	76	of	of	ADP
ap-4182	87	77	the	the	DET
ap-4182	87	78	phase	phase	NOUN
ap-4182	87	79	ϕn	ϕn	INTJ
ap-4182	87	80	,	,	PUNCT
ap-4182	87	81	j	j	PROPN
ap-4182	87	82	over	over	ADP
ap-4182	87	83	the	the	DET
ap-4182	87	84	borders	border	NOUN
ap-4182	87	85	of	of	ADP
ap-4182	87	86	the	the	DET
ap-4182	87	87	standard	standard	ADJ
ap-4182	87	88	interval	interval	NOUN
ap-4182	88	1	[	[	X
ap-4182	88	2	−π	−π	PROPN
ap-4182	88	3	,	,	PUNCT
ap-4182	88	4	π	π	PROPN
ap-4182	88	5	)	)	PUNCT
ap-4182	88	6	.	.	PUNCT
ap-4182	89	1	starting	start	VERB
ap-4182	89	2	with	with	ADP
ap-4182	89	3	x	x	SYM
ap-4182	89	4	=	=	SYM
ap-4182	89	5	0	0	NUM
ap-4182	89	6	we	we	PRON
ap-4182	89	7	increase	increase	VERB
ap-4182	89	8	x	x	PUNCT
ap-4182	89	9	by	by	ADP
ap-4182	89	10	one	one	NUM
ap-4182	89	11	for	for	ADP
ap-4182	89	12	every	every	DET
ap-4182	89	13	jump	jump	NOUN
ap-4182	89	14	of	of	ADP
ap-4182	89	15	ϕn	ϕn	INTJ
ap-4182	89	16	,	,	PUNCT
ap-4182	89	17	j	j	PROPN
ap-4182	89	18	from	from	ADP
ap-4182	89	19	−π	−π	NUM
ap-4182	89	20	to	to	ADP
ap-4182	89	21	π	π	PROPN
ap-4182	89	22	and	and	CCONJ
ap-4182	89	23	subtract	subtract	VERB
ap-4182	89	24	1	1	NUM
ap-4182	89	25	for	for	ADP
ap-4182	89	26	the	the	DET
ap-4182	89	27	opposite	opposite	ADJ
ap-4182	89	28	direction	direction	NOUN
ap-4182	89	29	.	.	PUNCT
ap-4182	90	1	the	the	DET
ap-4182	90	2	states	state	NOUN
ap-4182	90	3	of	of	ADP
ap-4182	90	4	the	the	DET
ap-4182	90	5	biorthogonal	biorthogonal	ADJ
ap-4182	90	6	basis	basis	NOUN
ap-4182	90	7	can	can	AUX
ap-4182	90	8	then	then	ADV
ap-4182	90	9	finally	finally	ADV
ap-4182	90	10	be	be	AUX
ap-4182	90	11	gauge	gauge	NOUN
ap-4182	90	12	-	-	PUNCT
ap-4182	90	13	smoothed	smooth	VERB
ap-4182	90	14	by	by	ADP
ap-4182	90	15	multiplying	multiply	VERB
ap-4182	90	16	the	the	DET
ap-4182	90	17	states	state	NOUN
ap-4182	90	18	at	at	ADP
ap-4182	90	19	αj	αj	NUM
ap-4182	90	20	by	by	ADP
ap-4182	90	21	a	a	DET
ap-4182	90	22	phase	phase	NOUN
ap-4182	90	23	factor	factor	NOUN
ap-4182	90	24	according	accord	VERB
ap-4182	90	25	to	to	ADP
ap-4182	90	26	〈	〈	PROPN
ap-4182	90	27	χn(αj)|	χn(αj)|	PRON
ap-4182	90	28	→	→	SYM
ap-4182	90	29	〈	〈	PROPN
ap-4182	90	30	χn(αj)|	χn(αj)|	VERB
ap-4182	90	31	e−if∆ϕn	e−if∆ϕn	PROPN
ap-4182	90	32	(	(	PUNCT
ap-4182	90	33	(	(	PUNCT
ap-4182	90	34	j−1)/(m−1	j−1)/(m−1	PROPN
ap-4182	90	35	)	)	PUNCT
ap-4182	90	36	)	)	PUNCT
ap-4182	90	37	,	,	PUNCT
ap-4182	90	38	(	(	PUNCT
ap-4182	90	39	10a	10a	NOUN
ap-4182	90	40	)	)	PUNCT
ap-4182	90	41	|φn(αj	|φn(αj	NOUN
ap-4182	90	42	)	)	PUNCT
ap-4182	90	43	〉	〉	PROPN
ap-4182	90	44	→	→	SYM
ap-4182	90	45	|φn(αj	|φn(αj	NOUN
ap-4182	90	46	)	)	PUNCT
ap-4182	90	47	〉	〉	PROPN
ap-4182	90	48	eif∆ϕn	eif∆ϕn	PROPN
ap-4182	90	49	(	(	PUNCT
ap-4182	90	50	(	(	PUNCT
ap-4182	90	51	j−1)/(m−1	j−1)/(m−1	PROPN
ap-4182	90	52	)	)	PUNCT
ap-4182	90	53	)	)	PUNCT
ap-4182	90	54	(	(	PUNCT
ap-4182	90	55	10b	10b	NOUN
ap-4182	90	56	)	)	PUNCT
ap-4182	90	57	for	for	ADP
ap-4182	90	58	j	j	PROPN
ap-4182	90	59	∈	∈	PROPN
ap-4182	90	60	{	{	PUNCT
ap-4182	90	61	1	1	NUM
ap-4182	90	62	,	,	PUNCT
ap-4182	90	63	...	...	PUNCT
ap-4182	90	64	,	,	PUNCT
ap-4182	90	65	m	m	VERB
ap-4182	90	66	}	}	PUNCT
ap-4182	90	67	,	,	PUNCT
ap-4182	90	68	where	where	SCONJ
ap-4182	90	69	f∆ϕn	f∆ϕn	NOUN
ap-4182	90	70	(	(	PUNCT
ap-4182	90	71	x	x	X
ap-4182	90	72	)	)	PUNCT
ap-4182	90	73	is	be	AUX
ap-4182	90	74	any	any	DET
ap-4182	90	75	“	"	PUNCT
ap-4182	90	76	smooth	smooth	ADJ
ap-4182	90	77	”	"	PUNCT
ap-4182	90	78	real	real	ADV
ap-4182	90	79	valued	value	VERB
ap-4182	90	80	continuous	continuous	ADJ
ap-4182	90	81	function	function	NOUN
ap-4182	90	82	f∆ϕn	f∆ϕn	NOUN
ap-4182	90	83	:	:	PUNCT
ap-4182	91	1	[	[	X
ap-4182	91	2	0	0	NUM
ap-4182	91	3	,	,	PUNCT
ap-4182	91	4	1]→	1]→	ADJ
ap-4182	91	5	r	r	NOUN
ap-4182	91	6	,	,	PUNCT
ap-4182	91	7	(	(	PUNCT
ap-4182	91	8	11a	11a	NOUN
ap-4182	91	9	)	)	PUNCT
ap-4182	91	10	fulfilling	fulfil	VERB
ap-4182	91	11	:	:	PUNCT
ap-4182	91	12	0	0	NUM
ap-4182	91	13	7→	7→	NUM
ap-4182	91	14	f∆ϕn	f∆ϕn	NOUN
ap-4182	91	15	(	(	PUNCT
ap-4182	91	16	0	0	NUM
ap-4182	91	17	)	)	PUNCT
ap-4182	91	18	=	=	SYM
ap-4182	91	19	0	0	NUM
ap-4182	91	20	,	,	PUNCT
ap-4182	91	21	1	1	NUM
ap-4182	91	22	7→	7→	NUM
ap-4182	91	23	f∆ϕn	f∆ϕn	NOUN
ap-4182	91	24	(	(	PUNCT
ap-4182	91	25	1	1	NUM
ap-4182	91	26	)	)	PUNCT
ap-4182	91	27	=	=	SYM
ap-4182	91	28	∆ϕn	∆ϕn	NOUN
ap-4182	91	29	±	±	NUM
ap-4182	91	30	2zπ	2zπ	NOUN
ap-4182	91	31	,	,	PUNCT
ap-4182	91	32	(	(	PUNCT
ap-4182	91	33	11b	11b	NOUN
ap-4182	91	34	)	)	PUNCT
ap-4182	91	35	with	with	ADP
ap-4182	91	36	z	z	PROPN
ap-4182	91	37	∈	∈	PROPN
ap-4182	91	38	z.	z.	X
ap-4182	91	39	its	its	PRON
ap-4182	91	40	explicit	explicit	ADJ
ap-4182	91	41	form	form	NOUN
ap-4182	91	42	is	be	AUX
ap-4182	91	43	not	not	PART
ap-4182	91	44	critical	critical	ADJ
ap-4182	91	45	since	since	SCONJ
ap-4182	91	46	it	it	PRON
ap-4182	91	47	only	only	ADV
ap-4182	91	48	has	have	VERB
ap-4182	91	49	to	to	PART
ap-4182	91	50	correct	correct	VERB
ap-4182	91	51	the	the	DET
ap-4182	91	52	total	total	ADJ
ap-4182	91	53	phase	phase	NOUN
ap-4182	91	54	change	change	NOUN
ap-4182	91	55	over	over	ADP
ap-4182	91	56	the	the	DET
ap-4182	91	57	whole	whole	ADJ
ap-4182	91	58	range	range	NOUN
ap-4182	91	59	of	of	ADP
ap-4182	91	60	the	the	DET
ap-4182	91	61	loop	loop	NOUN
ap-4182	91	62	.	.	PUNCT
ap-4182	92	1	however	however	ADV
ap-4182	92	2	,	,	PUNCT
ap-4182	92	3	a	a	DET
ap-4182	92	4	linear	linear	ADJ
ap-4182	92	5	progression	progression	NOUN
ap-4182	92	6	of	of	ADP
ap-4182	92	7	the	the	DET
ap-4182	92	8	phase	phase	NOUN
ap-4182	92	9	correction	correction	NOUN
ap-4182	92	10	from	from	ADP
ap-4182	92	11	step	step	NOUN
ap-4182	92	12	to	to	PART
ap-4182	92	13	step	step	NOUN
ap-4182	92	14	turns	turn	VERB
ap-4182	92	15	out	out	ADP
ap-4182	92	16	to	to	PART
ap-4182	92	17	be	be	AUX
ap-4182	92	18	a	a	DET
ap-4182	92	19	good	good	ADJ
ap-4182	92	20	choice	choice	NOUN
ap-4182	92	21	.	.	PUNCT
ap-4182	93	1	it	it	PRON
ap-4182	93	2	should	should	AUX
ap-4182	93	3	be	be	AUX
ap-4182	93	4	mentioned	mention	VERB
ap-4182	93	5	that	that	SCONJ
ap-4182	93	6	in	in	ADP
ap-4182	93	7	case	case	NOUN
ap-4182	93	8	of	of	ADP
ap-4182	93	9	a	a	DET
ap-4182	93	10	degeneracy	degeneracy	NOUN
ap-4182	93	11	of	of	ADP
ap-4182	93	12	the	the	DET
ap-4182	93	13	eigenvalue	eigenvalue	NOUN
ap-4182	93	14	at	at	ADP
ap-4182	93	15	αj	αj	ADP
ap-4182	93	16	the	the	DET
ap-4182	93	17	solution	solution	NOUN
ap-4182	93	18	of	of	ADP
ap-4182	93	19	(	(	PUNCT
ap-4182	93	20	5a	5a	NUM
ap-4182	93	21	)	)	PUNCT
ap-4182	93	22	and	and	CCONJ
ap-4182	93	23	(	(	PUNCT
ap-4182	93	24	5b	5b	NUM
ap-4182	93	25	)	)	PUNCT
ap-4182	93	26	yields	yield	VERB
ap-4182	93	27	an	an	DET
ap-4182	93	28	arbitrary	arbitrary	ADJ
ap-4182	93	29	linear	linear	ADJ
ap-4182	93	30	combination	combination	NOUN
ap-4182	93	31	of	of	ADP
ap-4182	93	32	eigenvectors	eigenvector	NOUN
ap-4182	93	33	of	of	ADP
ap-4182	93	34	the	the	DET
ap-4182	93	35	degenerate	degenerate	ADJ
ap-4182	93	36	eigenspace	eigenspace	NOUN
ap-4182	93	37	.	.	PUNCT
ap-4182	94	1	to	to	PART
ap-4182	94	2	find	find	VERB
ap-4182	94	3	the	the	DET
ap-4182	94	4	correct	correct	ADJ
ap-4182	94	5	eigenvectors	eigenvector	NOUN
ap-4182	94	6	〈	〈	PROPN
ap-4182	94	7	χn(αj)|	χn(αj)|	PUNCT
ap-4182	94	8	and	and	CCONJ
ap-4182	94	9	|φn(αj	|φn(αj	PROPN
ap-4182	94	10	)	)	PUNCT
ap-4182	94	11	〉	〉	NOUN
ap-4182	94	12	one	one	NOUN
ap-4182	94	13	can	can	AUX
ap-4182	94	14	apply	apply	VERB
ap-4182	94	15	a	a	DET
ap-4182	94	16	biorthogonal	biorthogonal	ADJ
ap-4182	94	17	gram	gram	NOUN
ap-4182	94	18	-	-	PUNCT
ap-4182	94	19	schmidt	schmidt	NOUN
ap-4182	94	20	algorithm	algorithm	NOUN
ap-4182	95	1	[	[	X
ap-4182	95	2	45	45	NUM
ap-4182	95	3	]	]	PUNCT
ap-4182	95	4	.	.	PUNCT
ap-4182	96	1	if	if	SCONJ
ap-4182	96	2	αj−1	αj−1	NOUN
ap-4182	96	3	is	be	AUX
ap-4182	96	4	a	a	DET
ap-4182	96	5	point	point	NOUN
ap-4182	96	6	neighbouring	neighbour	VERB
ap-4182	96	7	the	the	DET
ap-4182	96	8	degeneracy	degeneracy	NOUN
ap-4182	96	9	one	one	PRON
ap-4182	96	10	tries	try	VERB
ap-4182	96	11	to	to	PART
ap-4182	96	12	find	find	VERB
ap-4182	96	13	a	a	DET
ap-4182	96	14	linear	linear	ADJ
ap-4182	96	15	combination	combination	NOUN
ap-4182	96	16	of	of	ADP
ap-4182	96	17	the	the	DET
ap-4182	96	18	vectors	vector	NOUN
ap-4182	96	19	of	of	ADP
ap-4182	96	20	the	the	DET
ap-4182	96	21	left	left	ADJ
ap-4182	96	22	degenerate	degenerate	ADJ
ap-4182	96	23	eigenspace	eigenspace	NOUN
ap-4182	96	24	fulfilling	fulfil	VERB
ap-4182	96	25	〈	〈	PROPN
ap-4182	96	26	χm(αj)|φn(αj−1	χm(αj)|φn(αj−1	NOUN
ap-4182	96	27	)	)	PUNCT
ap-4182	96	28	〉	〉	PROPN
ap-4182	96	29	≈	≈	PROPN
ap-4182	96	30	δmn	δmn	NOUN
ap-4182	96	31	(	(	PUNCT
ap-4182	96	32	12	12	NUM
ap-4182	96	33	)	)	PUNCT
ap-4182	96	34	and	and	CCONJ
ap-4182	96	35	then	then	ADV
ap-4182	96	36	chooses	choose	VERB
ap-4182	96	37	the	the	DET
ap-4182	96	38	right	right	ADJ
ap-4182	96	39	eigenvectors	eigenvector	NOUN
ap-4182	96	40	such	such	ADJ
ap-4182	96	41	that	that	SCONJ
ap-4182	96	42	〈	〈	PROPN
ap-4182	96	43	χm(αj)|φn(αj	χm(αj)|φn(αj	ADJ
ap-4182	96	44	)	)	PUNCT
ap-4182	96	45	〉	〉	PROPN
ap-4182	96	46	=	=	SYM
ap-4182	96	47	δmn	δmn	NOUN
ap-4182	96	48	.	.	PUNCT
ap-4182	97	1	(	(	PUNCT
ap-4182	97	2	13	13	NUM
ap-4182	97	3	)	)	PUNCT
ap-4182	97	4	alternatively	alternatively	ADV
ap-4182	97	5	one	one	PRON
ap-4182	97	6	can	can	AUX
ap-4182	97	7	treat	treat	VERB
ap-4182	97	8	the	the	DET
ap-4182	97	9	real	real	ADJ
ap-4182	97	10	and	and	CCONJ
ap-4182	97	11	imaginary	imaginary	ADJ
ap-4182	97	12	parts	part	NOUN
ap-4182	97	13	of	of	ADP
ap-4182	97	14	the	the	DET
ap-4182	97	15	degenerate	degenerate	ADJ
ap-4182	97	16	eigenvector	eigenvector	NOUN
ap-4182	97	17	components	component	NOUN
ap-4182	97	18	as	as	ADP
ap-4182	97	19	“	"	PUNCT
ap-4182	97	20	smooth	smooth	ADJ
ap-4182	97	21	”	"	PUNCT
ap-4182	97	22	functions	function	NOUN
ap-4182	97	23	.	.	PUNCT
ap-4182	98	1	then	then	ADV
ap-4182	98	2	the	the	DET
ap-4182	98	3	eigenvector	eigenvector	NOUN
ap-4182	98	4	components	component	NOUN
ap-4182	98	5	at	at	ADP
ap-4182	98	6	degeneracy	degeneracy	PROPN
ap-4182	98	7	points	point	NOUN
ap-4182	98	8	can	can	AUX
ap-4182	98	9	be	be	AUX
ap-4182	98	10	predicted	predict	VERB
ap-4182	98	11	by	by	ADP
ap-4182	98	12	fitting	fit	VERB
ap-4182	98	13	a	a	DET
ap-4182	98	14	spline	spline	NOUN
ap-4182	98	15	to	to	ADP
ap-4182	98	16	the	the	DET
ap-4182	98	17	vector	vector	NOUN
ap-4182	98	18	components	component	NOUN
ap-4182	98	19	at	at	ADP
ap-4182	98	20	neighbouring	neighbouring	ADJ
ap-4182	98	21	points	point	NOUN
ap-4182	98	22	αl	αl	ADP
ap-4182	98	23	.	.	PUNCT
ap-4182	99	1	an	an	DET
ap-4182	99	2	approximation	approximation	NOUN
ap-4182	99	3	to	to	ADP
ap-4182	99	4	the	the	DET
ap-4182	99	5	correct	correct	ADJ
ap-4182	99	6	eigenvectors	eigenvector	NOUN
ap-4182	99	7	of	of	ADP
ap-4182	99	8	the	the	DET
ap-4182	99	9	degenerate	degenerate	ADJ
ap-4182	99	10	eigenspace	eigenspace	NOUN
ap-4182	99	11	can	can	AUX
ap-4182	99	12	be	be	AUX
ap-4182	99	13	determined	determine	VERB
ap-4182	99	14	by	by	ADP
ap-4182	99	15	a	a	DET
ap-4182	99	16	linear	linear	ADJ
ap-4182	99	17	combination	combination	NOUN
ap-4182	99	18	of	of	ADP
ap-4182	99	19	the	the	DET
ap-4182	99	20	obtained	obtain	VERB
ap-4182	99	21	vectors	vector	NOUN
ap-4182	99	22	of	of	ADP
ap-4182	99	23	the	the	DET
ap-4182	99	24	degenerate	degenerate	ADJ
ap-4182	99	25	eigenspace	eigenspace	NOUN
ap-4182	99	26	such	such	ADJ
ap-4182	99	27	that	that	SCONJ
ap-4182	99	28	they	they	PRON
ap-4182	99	29	fit	fit	VERB
ap-4182	99	30	best	good	ADJ
ap-4182	99	31	to	to	ADP
ap-4182	99	32	the	the	DET
ap-4182	99	33	prediction	prediction	NOUN
ap-4182	99	34	.	.	PUNCT
ap-4182	100	1	hermitian	hermitian	ADJ
ap-4182	100	2	hamiltonians	hamiltonian	NOUN
ap-4182	100	3	can	can	AUX
ap-4182	100	4	be	be	AUX
ap-4182	100	5	treated	treat	VERB
ap-4182	100	6	as	as	ADP
ap-4182	100	7	a	a	DET
ap-4182	100	8	special	special	ADJ
ap-4182	100	9	case	case	NOUN
ap-4182	100	10	,	,	PUNCT
ap-4182	100	11	in	in	ADP
ap-4182	100	12	which	which	PRON
ap-4182	100	13	the	the	DET
ap-4182	100	14	left	left	ADJ
ap-4182	100	15	eigenvector	eigenvector	NOUN
ap-4182	100	16	fulfils	fulfil	NOUN
ap-4182	100	17	〈	〈	PROPN
ap-4182	100	18	χn|	χn|	PROPN
ap-4182	100	19	=	=	SYM
ap-4182	100	20	(	(	PUNCT
ap-4182	100	21	|φn〉t)∗.	|φn〉t)∗.	PROPN
ap-4182	100	22	4	4	NUM
ap-4182	100	23	.	.	X
ap-4182	100	24	application	application	NOUN
ap-4182	100	25	to	to	ADP
ap-4182	100	26	a	a	DET
ap-4182	100	27	one	one	NUM
ap-4182	100	28	-	-	PUNCT
ap-4182	100	29	dimensional	dimensional	ADJ
ap-4182	100	30	lattice	lattice	NOUN
ap-4182	100	31	system	system	NOUN
ap-4182	100	32	in	in	ADP
ap-4182	100	33	this	this	DET
ap-4182	100	34	section	section	NOUN
ap-4182	100	35	we	we	PRON
ap-4182	100	36	apply	apply	VERB
ap-4182	100	37	the	the	DET
ap-4182	100	38	gauge	gauge	NOUN
ap-4182	100	39	smoothing	smoothing	NOUN
ap-4182	100	40	procedure	procedure	NOUN
ap-4182	100	41	developed	develop	VERB
ap-4182	100	42	in	in	ADP
ap-4182	100	43	section	section	NOUN
ap-4182	100	44	3	3	NUM
ap-4182	100	45	to	to	ADP
ap-4182	100	46	a	a	DET
ap-4182	100	47	pt	pt	NOUN
ap-4182	100	48	-symmetric	-symmetric	ADJ
ap-4182	100	49	onedimensional	onedimensional	ADJ
ap-4182	100	50	lattice	lattice	NOUN
ap-4182	100	51	system	system	NOUN
ap-4182	100	52	to	to	PART
ap-4182	100	53	calculate	calculate	VERB
ap-4182	100	54	the	the	DET
ap-4182	100	55	complex	complex	ADJ
ap-4182	100	56	zak	zak	PROPN
ap-4182	100	57	phase	phase	NOUN
ap-4182	100	58	γn	γn	NOUN
ap-4182	100	59	=	=	SYM
ap-4182	100	60	∮	∮	NUM
ap-4182	100	61	bz	bz	PROPN
ap-4182	100	62	〈	〈	PROPN
ap-4182	100	63	χn|∂k|φn〉dk	χn|∂k|φn〉dk	PROPN
ap-4182	100	64	,	,	PUNCT
ap-4182	100	65	(	(	PUNCT
ap-4182	100	66	14	14	NUM
ap-4182	100	67	)	)	PUNCT
ap-4182	100	68	where	where	SCONJ
ap-4182	100	69	the	the	DET
ap-4182	100	70	parameter	parameter	NOUN
ap-4182	100	71	space	space	NOUN
ap-4182	100	72	is	be	AUX
ap-4182	100	73	given	give	VERB
ap-4182	100	74	by	by	ADP
ap-4182	100	75	the	the	DET
ap-4182	100	76	discretised	discretise	VERB
ap-4182	100	77	brillouin	brillouin	NOUN
ap-4182	100	78	zone	zone	NOUN
ap-4182	100	79	bz	bz	PROPN
ap-4182	100	80	and	and	CCONJ
ap-4182	100	81	k	k	PROPN
ap-4182	100	82	is	be	AUX
ap-4182	100	83	the	the	DET
ap-4182	100	84	wave	wave	NOUN
ap-4182	100	85	number	number	NOUN
ap-4182	100	86	.	.	PUNCT
ap-4182	101	1	as	as	ADP
ap-4182	101	2	an	an	DET
ap-4182	101	3	example	example	NOUN
ap-4182	101	4	we	we	PRON
ap-4182	101	5	consider	consider	VERB
ap-4182	101	6	the	the	DET
ap-4182	101	7	ssh	ssh	NOUN
ap-4182	101	8	model	model	NOUN
ap-4182	102	1	[	[	X
ap-4182	102	2	41	41	NUM
ap-4182	102	3	]	]	PUNCT
ap-4182	102	4	with	with	ADP
ap-4182	102	5	n	n	PROPN
ap-4182	102	6	lattice	lattice	NOUN
ap-4182	102	7	sites	site	NOUN
ap-4182	102	8	,	,	PUNCT
ap-4182	102	9	tunnelling	tunnelling	NOUN
ap-4182	102	10	amplitudes	amplitude	NOUN
ap-4182	102	11	t+	t+	NUM
ap-4182	102	12	and	and	CCONJ
ap-4182	102	13	t−	t−	PROPN
ap-4182	102	14	,	,	PUNCT
ap-4182	102	15	and	and	CCONJ
ap-4182	102	16	creation	creation	NOUN
ap-4182	102	17	(	(	PUNCT
ap-4182	102	18	annihilation	annihilation	NOUN
ap-4182	102	19	)	)	PUNCT
ap-4182	102	20	operators	operator	NOUN
ap-4182	102	21	of	of	ADP
ap-4182	102	22	spinless	spinless	ADJ
ap-4182	102	23	fermions	fermion	NOUN
ap-4182	102	24	c†n	c†n	NUM
ap-4182	102	25	(	(	PUNCT
ap-4182	102	26	cn	cn	NOUN
ap-4182	102	27	)	)	PUNCT
ap-4182	102	28	at	at	ADP
ap-4182	102	29	site	site	NOUN
ap-4182	102	30	n	n	CCONJ
ap-4182	102	31	,	,	PUNCT
ap-4182	102	32	hssh	hssh	NOUN
ap-4182	102	33	=	=	NOUN
ap-4182	102	34	n/2∑	n/2∑	PROPN
ap-4182	102	35	n=1	n=1	PUNCT
ap-4182	102	36	t−	t−	PROPN
ap-4182	102	37	(	(	PUNCT
ap-4182	102	38	c†an	c†an	PROPN
ap-4182	102	39	cbn	cbn	PROPN
ap-4182	102	40	+	+	X
ap-4182	102	41	h.c	h.c	PROPN
ap-4182	102	42	.	.	PUNCT
ap-4182	102	43	)	)	PUNCT
ap-4182	103	1	+	+	CCONJ
ap-4182	103	2	n/2−1∑	n/2−1∑	X
ap-4182	103	3	n=1	n=1	PROPN
ap-4182	103	4	t+	t+	NOUN
ap-4182	103	5	(	(	PUNCT
ap-4182	103	6	c†bn	c†bn	PROPN
ap-4182	103	7	can+1	can+1	PROPN
ap-4182	103	8	+	+	X
ap-4182	103	9	h.c	h.c	PROPN
ap-4182	103	10	.	.	PUNCT
ap-4182	103	11	)	)	PUNCT
ap-4182	103	12	.	.	PUNCT
ap-4182	104	1	(	(	PUNCT
ap-4182	104	2	15	15	X
ap-4182	104	3	)	)	PUNCT
ap-4182	104	4	we	we	PRON
ap-4182	104	5	apply	apply	VERB
ap-4182	104	6	an	an	DET
ap-4182	104	7	alternating	alternate	VERB
ap-4182	104	8	non	non	ADJ
ap-4182	104	9	-	-	ADJ
ap-4182	104	10	hermitian	hermitian	ADJ
ap-4182	104	11	pt	pt	ADJ
ap-4182	104	12	-symmetric	-symmetric	ADJ
ap-4182	104	13	potential	potential	NOUN
ap-4182	104	14	of	of	ADP
ap-4182	104	15	the	the	DET
ap-4182	104	16	form	form	NOUN
ap-4182	104	17	u	u	NOUN
ap-4182	104	18	=	=	NOUN
ap-4182	104	19	iγ2	iγ2	NOUN
ap-4182	104	20	n/2∑	n/2∑	NOUN
ap-4182	104	21	n=1	n=1	PROPN
ap-4182	104	22	(	(	PUNCT
ap-4182	104	23	c†bn	c†bn	PROPN
ap-4182	104	24	cbn	cbn	PROPN
ap-4182	104	25	−	−	PROPN
ap-4182	104	26	c†an	c†an	VERB
ap-4182	104	27	can	can	AUX
ap-4182	104	28	)	)	PUNCT
ap-4182	104	29	,	,	PUNCT
ap-4182	104	30	(	(	PUNCT
ap-4182	104	31	16	16	NUM
ap-4182	104	32	)	)	PUNCT
ap-4182	104	33	where	where	SCONJ
ap-4182	104	34	γ	γ	PROPN
ap-4182	104	35	denotes	denote	VERB
ap-4182	104	36	the	the	DET
ap-4182	104	37	parameter	parameter	NOUN
ap-4182	104	38	of	of	ADP
ap-4182	104	39	gain	gain	NOUN
ap-4182	104	40	and	and	CCONJ
ap-4182	104	41	loss	loss	NOUN
ap-4182	104	42	.	.	PUNCT
ap-4182	105	1	the	the	DET
ap-4182	105	2	pt	pt	NOUN
ap-4182	105	3	-symmetric	-symmetric	ADJ
ap-4182	105	4	hamiltonian	hamiltonian	NOUN
ap-4182	105	5	describing	describe	VERB
ap-4182	105	6	this	this	DET
ap-4182	105	7	model	model	NOUN
ap-4182	105	8	(	(	PUNCT
ap-4182	105	9	sketched	sketch	VERB
ap-4182	105	10	in	in	ADP
ap-4182	105	11	figure	figure	NOUN
ap-4182	105	12	1	1	NUM
ap-4182	105	13	)	)	PUNCT
ap-4182	105	14	is	be	AUX
ap-4182	105	15	given	give	VERB
ap-4182	105	16	by	by	ADP
ap-4182	105	17	h	h	NOUN
ap-4182	105	18	=	=	PUNCT
ap-4182	105	19	hssh	hssh	PROPN
ap-4182	105	20	+	+	CCONJ
ap-4182	105	21	u.	u.	NOUN
ap-4182	105	22	(	(	PUNCT
ap-4182	105	23	17	17	NUM
ap-4182	105	24	)	)	PUNCT
ap-4182	105	25	to	to	PART
ap-4182	105	26	evaluate	evaluate	VERB
ap-4182	105	27	(	(	PUNCT
ap-4182	105	28	14	14	NUM
ap-4182	105	29	)	)	PUNCT
ap-4182	105	30	we	we	PRON
ap-4182	105	31	need	need	VERB
ap-4182	105	32	to	to	PART
ap-4182	105	33	represent	represent	VERB
ap-4182	105	34	this	this	DET
ap-4182	105	35	hamiltonian	hamiltonian	NOUN
ap-4182	105	36	in	in	ADP
ap-4182	105	37	the	the	DET
ap-4182	105	38	reciprocal	reciprocal	ADJ
ap-4182	105	39	space	space	NOUN
ap-4182	105	40	,	,	PUNCT
ap-4182	105	41	where	where	SCONJ
ap-4182	105	42	the	the	DET
ap-4182	105	43	brillouin	brillouin	NOUN
ap-4182	105	44	zone	zone	NOUN
ap-4182	105	45	472	472	NUM
ap-4182	105	46	vol	vol	NOUN
ap-4182	105	47	.	.	PUNCT
ap-4182	106	1	57	57	NUM
ap-4182	106	2	no	no	NOUN
ap-4182	106	3	.	.	PUNCT
ap-4182	107	1	6/2017	6/2017	NUM
ap-4182	107	2	numerical	numerical	ADJ
ap-4182	107	3	calculation	calculation	NOUN
ap-4182	107	4	of	of	ADP
ap-4182	107	5	the	the	DET
ap-4182	107	6	complex	complex	ADJ
ap-4182	107	7	berry	berry	NOUN
ap-4182	107	8	phase	phase	NOUN
ap-4182	107	9	t−	t−	PROPN
ap-4182	107	10	t+	t+	NOUN
ap-4182	107	11	t−	t−	ADP
ap-4182	107	12	t−	t−	PROPN
ap-4182	107	13	a1	a1	NOUN
ap-4182	107	14	b1	b1	PROPN
ap-4182	107	15	a2	a2	PROPN
ap-4182	107	16	b2	b2	PROPN
ap-4182	107	17	an/2	an/2	PROPN
ap-4182	107	18	bn/2	bn/2	PROPN
ap-4182	107	19	figure	figure	NOUN
ap-4182	107	20	1	1	NUM
ap-4182	107	21	.	.	PUNCT
ap-4182	108	1	(	(	PUNCT
ap-4182	108	2	colour	colour	NOUN
ap-4182	108	3	online	online	NOUN
ap-4182	108	4	)	)	PUNCT
ap-4182	108	5	sketch	sketch	NOUN
ap-4182	108	6	of	of	ADP
ap-4182	108	7	the	the	DET
ap-4182	108	8	ssh	ssh	NOUN
ap-4182	108	9	model	model	NOUN
ap-4182	108	10	with	with	ADP
ap-4182	108	11	n	n	ADP
ap-4182	108	12	lattice	lattice	NOUN
ap-4182	108	13	sites	site	NOUN
ap-4182	108	14	subject	subject	ADJ
ap-4182	108	15	to	to	ADP
ap-4182	108	16	the	the	DET
ap-4182	108	17	alternating	alternate	VERB
ap-4182	108	18	imaginary	imaginary	ADJ
ap-4182	108	19	potential	potential	ADJ
ap-4182	108	20	u	u	NOUN
ap-4182	108	21	.	.	PUNCT
ap-4182	109	1	the	the	DET
ap-4182	109	2	minus	minus	ADJ
ap-4182	109	3	(	(	PUNCT
ap-4182	109	4	plus	plus	CCONJ
ap-4182	109	5	)	)	PUNCT
ap-4182	109	6	sign	sign	NOUN
ap-4182	109	7	marks	mark	VERB
ap-4182	109	8	a	a	DET
ap-4182	109	9	negative	negative	ADJ
ap-4182	109	10	(	(	PUNCT
ap-4182	109	11	positive	positive	ADJ
ap-4182	109	12	)	)	PUNCT
ap-4182	109	13	imaginary	imaginary	ADJ
ap-4182	109	14	potential	potential	NOUN
ap-4182	109	15	corresponding	correspond	VERB
ap-4182	109	16	to	to	ADP
ap-4182	109	17	particle	particle	NOUN
ap-4182	109	18	sinks	sink	NOUN
ap-4182	109	19	(	(	PUNCT
ap-4182	109	20	sources	source	NOUN
ap-4182	109	21	)	)	PUNCT
ap-4182	109	22	.	.	PUNCT
ap-4182	110	1	acts	act	NOUN
ap-4182	110	2	as	as	ADP
ap-4182	110	3	parameter	parameter	NOUN
ap-4182	110	4	space	space	NOUN
ap-4182	110	5	.	.	PUNCT
ap-4182	111	1	this	this	PRON
ap-4182	111	2	is	be	AUX
ap-4182	111	3	done	do	VERB
ap-4182	111	4	by	by	ADP
ap-4182	111	5	rewriting	rewrite	VERB
ap-4182	111	6	the	the	DET
ap-4182	111	7	hamiltonian	hamiltonian	NOUN
ap-4182	111	8	with	with	ADP
ap-4182	111	9	creation	creation	NOUN
ap-4182	111	10	and	and	CCONJ
ap-4182	111	11	annihilation	annihilation	NOUN
ap-4182	111	12	operators	operator	NOUN
ap-4182	111	13	in	in	ADP
ap-4182	111	14	the	the	DET
ap-4182	111	15	reciprocal	reciprocal	ADJ
ap-4182	111	16	space	space	NOUN
ap-4182	111	17	in	in	ADP
ap-4182	111	18	the	the	DET
ap-4182	111	19	limit	limit	NOUN
ap-4182	111	20	n	n	X
ap-4182	111	21	→∞	→∞	NOUN
ap-4182	111	22	,	,	PUNCT
ap-4182	111	23	h	h	NOUN
ap-4182	111	24	=	=	SYM
ap-4182	111	25	π∑	π∑	PROPN
ap-4182	111	26	k=−π	k=−π	PROPN
ap-4182	111	27	(	(	PUNCT
ap-4182	111	28	c†a	c†a	PROPN
ap-4182	111	29	,	,	PUNCT
ap-4182	111	30	k	k	PROPN
ap-4182	111	31	,	,	PUNCT
ap-4182	111	32	c	c	PROPN
ap-4182	111	33	†	†	PROPN
ap-4182	111	34	b	b	PROPN
ap-4182	111	35	,	,	PUNCT
ap-4182	111	36	k	k	PROPN
ap-4182	111	37	)	)	PUNCT
ap-4182	111	38	(	(	PUNCT
ap-4182	111	39	−iγ/2	−iγ/2	NUM
ap-4182	111	40	t−	t−	PROPN
ap-4182	111	41	+	+	PROPN
ap-4182	111	42	t+eik	t+eik	PROPN
ap-4182	111	43	t−	t−	NOUN
ap-4182	111	44	+	+	NOUN
ap-4182	112	1	t+e−ik	t+e−ik	NOUN
ap-4182	112	2	iγ/2	iγ/2	NOUN
ap-4182	112	3	)	)	PUNCT
ap-4182	112	4	(	(	PUNCT
ap-4182	112	5	ca	ca	PROPN
ap-4182	112	6	,	,	PUNCT
ap-4182	112	7	k	k	PROPN
ap-4182	112	8	cb	cb	PROPN
ap-4182	112	9	,	,	PUNCT
ap-4182	112	10	k	k	PROPN
ap-4182	112	11	)	)	PUNCT
ap-4182	112	12	,	,	PUNCT
ap-4182	112	13	(	(	PUNCT
ap-4182	112	14	18	18	NUM
ap-4182	112	15	)	)	PUNCT
ap-4182	112	16	where	where	SCONJ
ap-4182	112	17	the	the	DET
ap-4182	112	18	sum	sum	NOUN
ap-4182	112	19	runs	run	VERB
ap-4182	112	20	over	over	ADP
ap-4182	112	21	discrete	discrete	ADJ
ap-4182	112	22	values	value	NOUN
ap-4182	112	23	of	of	ADP
ap-4182	112	24	k	k	PROPN
ap-4182	112	25	in	in	ADP
ap-4182	112	26	steps	step	NOUN
ap-4182	112	27	of	of	ADP
ap-4182	112	28	k	k	NOUN
ap-4182	112	29	=	=	PUNCT
ap-4182	112	30	2π	2π	NOUN
ap-4182	112	31	/	/	SYM
ap-4182	112	32	n	n	CCONJ
ap-4182	112	33	and	and	CCONJ
ap-4182	112	34	the	the	DET
ap-4182	112	35	annihilation	annihilation	NOUN
ap-4182	112	36	operator	operator	NOUN
ap-4182	112	37	of	of	ADP
ap-4182	112	38	an	an	DET
ap-4182	112	39	electron	electron	NOUN
ap-4182	112	40	with	with	ADP
ap-4182	112	41	wave	wave	NOUN
ap-4182	112	42	number	number	NOUN
ap-4182	112	43	k	k	PROPN
ap-4182	112	44	is	be	AUX
ap-4182	112	45	given	give	VERB
ap-4182	112	46	by	by	ADP
ap-4182	112	47	cn	cn	PROPN
ap-4182	112	48	=	=	PROPN
ap-4182	112	49	1√	1√	PROPN
ap-4182	112	50	n	n	ADP
ap-4182	112	51	∑	∑	PROPN
ap-4182	112	52	k	k	PROPN
ap-4182	112	53	cke	cke	PROPN
ap-4182	112	54	−ikrn	−ikrn	PROPN
ap-4182	112	55	(	(	PUNCT
ap-4182	112	56	19	19	NUM
ap-4182	112	57	)	)	PUNCT
ap-4182	112	58	with	with	ADP
ap-4182	112	59	rn	rn	PROPN
ap-4182	112	60	=	=	SYM
ap-4182	112	61	an	an	PROPN
ap-4182	112	62	and	and	CCONJ
ap-4182	112	63	the	the	DET
ap-4182	112	64	lattice	lattice	NOUN
ap-4182	112	65	spacing	space	VERB
ap-4182	112	66	a.	a.	NOUN
ap-4182	112	67	the	the	DET
ap-4182	112	68	matrix	matrix	NOUN
ap-4182	112	69	occurring	occur	VERB
ap-4182	112	70	in	in	ADP
ap-4182	112	71	(	(	PUNCT
ap-4182	112	72	18	18	NUM
ap-4182	112	73	)	)	PUNCT
ap-4182	112	74	is	be	AUX
ap-4182	112	75	the	the	DET
ap-4182	112	76	bloch	bloch	PROPN
ap-4182	112	77	hamiltonian	hamiltonian	PROPN
ap-4182	112	78	h(k	h(k	PROPN
ap-4182	112	79	)	)	PUNCT
ap-4182	112	80	of	of	ADP
ap-4182	112	81	the	the	DET
ap-4182	112	82	system	system	NOUN
ap-4182	112	83	,	,	PUNCT
ap-4182	112	84	which	which	PRON
ap-4182	112	85	can	can	AUX
ap-4182	112	86	be	be	AUX
ap-4182	112	87	decomposed	decompose	VERB
ap-4182	112	88	into	into	ADP
ap-4182	112	89	the	the	DET
ap-4182	112	90	pauli	pauli	PROPN
ap-4182	112	91	matrices	matrix	NOUN
ap-4182	112	92	,	,	PUNCT
ap-4182	112	93	h(k	h(k	PROPN
ap-4182	112	94	)	)	PUNCT
ap-4182	113	1	=	=	NOUN
ap-4182	113	2	(	(	PUNCT
ap-4182	113	3	t−	t−	PROPN
ap-4182	113	4	+	+	NOUN
ap-4182	113	5	t+cos(k	t+cos(k	NOUN
ap-4182	113	6	)	)	PUNCT
ap-4182	113	7	)	)	PUNCT
ap-4182	114	1	σ1	σ1	PROPN
ap-4182	114	2	−	−	PROPN
ap-4182	114	3	t+sin(k)σ2	t+sin(k)σ2	PROPN
ap-4182	114	4	−	−	PROPN
ap-4182	114	5	iγ/2σ3	iγ/2σ3	PROPN
ap-4182	114	6	=	=	SYM
ap-4182	114	7	n(k	n(k	PROPN
ap-4182	114	8	)	)	PUNCT
ap-4182	114	9	·	·	PUNCT
ap-4182	115	1	σ	σ	NOUN
ap-4182	115	2	(	(	PUNCT
ap-4182	115	3	20	20	NUM
ap-4182	115	4	)	)	PUNCT
ap-4182	115	5	with	with	ADP
ap-4182	115	6	a	a	DET
ap-4182	115	7	coefficient	coefficient	NOUN
ap-4182	115	8	vector	vector	NOUN
ap-4182	115	9	n	n	NOUN
ap-4182	115	10	and	and	CCONJ
ap-4182	115	11	the	the	DET
ap-4182	115	12	pauli	pauli	PROPN
ap-4182	115	13	vector	vector	PROPN
ap-4182	115	14	σ	σ	PROPN
ap-4182	115	15	.	.	PROPN
ap-4182	116	1	from	from	ADP
ap-4182	116	2	this	this	DET
ap-4182	116	3	form	form	NOUN
ap-4182	116	4	the	the	DET
ap-4182	116	5	energy	energy	NOUN
ap-4182	116	6	eigenvalues	eigenvalue	NOUN
ap-4182	116	7	can	can	AUX
ap-4182	116	8	be	be	AUX
ap-4182	116	9	obtained	obtain	VERB
ap-4182	116	10	explicitly	explicitly	ADV
ap-4182	116	11	,	,	PUNCT
ap-4182	116	12	e±(k	e±(k	PROPN
ap-4182	116	13	)	)	PUNCT
ap-4182	116	14	=	=	SYM
ap-4182	116	15	±|n(k)|	±|n(k)|	NOUN
ap-4182	116	16	.	.	PUNCT
ap-4182	117	1	(	(	PUNCT
ap-4182	117	2	21	21	NUM
ap-4182	117	3	)	)	PUNCT
ap-4182	117	4	in	in	ADP
ap-4182	117	5	the	the	DET
ap-4182	117	6	limit	limit	NOUN
ap-4182	117	7	γ	γ	X
ap-4182	117	8	→	→	SYM
ap-4182	117	9	0	0	NUM
ap-4182	117	10	the	the	DET
ap-4182	117	11	hamiltonian	hamiltonian	NOUN
ap-4182	117	12	from	from	ADP
ap-4182	117	13	(	(	PUNCT
ap-4182	117	14	18	18	NUM
ap-4182	117	15	)	)	PUNCT
ap-4182	117	16	reproduces	reproduce	VERB
ap-4182	117	17	the	the	DET
ap-4182	117	18	hermitian	hermitian	ADJ
ap-4182	117	19	ssh	ssh	NOUN
ap-4182	117	20	model	model	NOUN
ap-4182	117	21	,	,	PUNCT
ap-4182	117	22	which	which	PRON
ap-4182	117	23	possesses	possess	VERB
ap-4182	117	24	time	time	NOUN
ap-4182	117	25	-	-	PUNCT
ap-4182	117	26	reversal	reversal	NOUN
ap-4182	117	27	,	,	PUNCT
ap-4182	117	28	reflection	reflection	NOUN
ap-4182	117	29	,	,	PUNCT
ap-4182	117	30	particle	particle	NOUN
ap-4182	117	31	-	-	PUNCT
ap-4182	117	32	hole	hole	NOUN
ap-4182	117	33	,	,	PUNCT
ap-4182	117	34	and	and	CCONJ
ap-4182	117	35	a	a	DET
ap-4182	117	36	chiral	chiral	ADJ
ap-4182	117	37	symmetry	symmetry	NOUN
ap-4182	117	38	(	(	PUNCT
ap-4182	117	39	represented	represent	VERB
ap-4182	117	40	by	by	ADP
ap-4182	117	41	σ3	σ3	PROPN
ap-4182	117	42	)	)	PUNCT
ap-4182	117	43	.	.	PUNCT
ap-4182	118	1	the	the	DET
ap-4182	118	2	introduction	introduction	NOUN
ap-4182	118	3	of	of	ADP
ap-4182	118	4	a	a	DET
ap-4182	118	5	pt	pt	NOUN
ap-4182	118	6	-symmetric	-symmetric	ADJ
ap-4182	118	7	non	non	ADJ
ap-4182	118	8	-	-	ADJ
ap-4182	118	9	hermitian	hermitian	ADJ
ap-4182	118	10	on	on	ADP
ap-4182	118	11	-	-	PUNCT
ap-4182	118	12	site	site	NOUN
ap-4182	118	13	potential	potential	NOUN
ap-4182	118	14	γ	γ	X
ap-4182	118	15	breaks	break	VERB
ap-4182	118	16	these	these	DET
ap-4182	118	17	symmetries	symmetry	NOUN
ap-4182	118	18	.	.	PUNCT
ap-4182	119	1	the	the	DET
ap-4182	119	2	non	non	ADJ
ap-4182	119	3	-	-	ADJ
ap-4182	119	4	hermitian	hermitian	ADJ
ap-4182	119	5	bloch	bloch	PROPN
ap-4182	119	6	hamiltonian	hamiltonian	PROPN
ap-4182	119	7	is	be	AUX
ap-4182	119	8	invariant	invariant	ADJ
ap-4182	119	9	under	under	ADP
ap-4182	119	10	the	the	DET
ap-4182	119	11	combined	combine	VERB
ap-4182	119	12	action	action	NOUN
ap-4182	119	13	of	of	ADP
ap-4182	119	14	the	the	DET
ap-4182	119	15	parity	parity	NOUN
ap-4182	119	16	and	and	CCONJ
ap-4182	119	17	the	the	DET
ap-4182	119	18	time	time	NOUN
ap-4182	119	19	inversion	inversion	NOUN
ap-4182	119	20	operator	operator	NOUN
ap-4182	119	21	.	.	PUNCT
ap-4182	120	1	further	far	ADV
ap-4182	120	2	the	the	DET
ap-4182	120	3	particle	particle	NOUN
ap-4182	120	4	-	-	PUNCT
ap-4182	120	5	hole	hole	NOUN
ap-4182	120	6	symmetry	symmetry	NOUN
ap-4182	120	7	is	be	AUX
ap-4182	120	8	broken	break	VERB
ap-4182	120	9	because	because	SCONJ
ap-4182	120	10	the	the	DET
ap-4182	120	11	sources	source	NOUN
ap-4182	120	12	(	(	PUNCT
ap-4182	120	13	sinks	sink	NOUN
ap-4182	120	14	)	)	PUNCT
ap-4182	120	15	of	of	ADP
ap-4182	120	16	an	an	DET
ap-4182	120	17	electron	electron	NOUN
ap-4182	120	18	correspond	correspond	NOUN
ap-4182	120	19	to	to	ADP
ap-4182	120	20	sinks	sink	NOUN
ap-4182	120	21	(	(	PUNCT
ap-4182	120	22	sources	source	NOUN
ap-4182	120	23	)	)	PUNCT
ap-4182	120	24	of	of	ADP
ap-4182	120	25	holes	hole	NOUN
ap-4182	120	26	.	.	PUNCT
ap-4182	121	1	the	the	DET
ap-4182	121	2	non	non	ADJ
ap-4182	121	3	-	-	ADJ
ap-4182	121	4	hermitian	hermitian	ADJ
ap-4182	121	5	system	system	NOUN
ap-4182	121	6	is	be	AUX
ap-4182	121	7	therefore	therefore	ADV
ap-4182	121	8	symmetric	symmetric	ADJ
ap-4182	121	9	under	under	ADP
ap-4182	121	10	the	the	DET
ap-4182	121	11	action	action	NOUN
ap-4182	121	12	of	of	ADP
ap-4182	121	13	the	the	DET
ap-4182	121	14	combination	combination	NOUN
ap-4182	121	15	of	of	ADP
ap-4182	121	16	the	the	DET
ap-4182	121	17	parity	parity	NOUN
ap-4182	121	18	and	and	CCONJ
ap-4182	121	19	the	the	DET
ap-4182	121	20	charge	charge	NOUN
ap-4182	121	21	conjugation	conjugation	NOUN
ap-4182	121	22	operator	operator	NOUN
ap-4182	121	23	.	.	PUNCT
ap-4182	122	1	further	far	ADV
ap-4182	122	2	it	it	PRON
ap-4182	122	3	has	have	VERB
ap-4182	122	4	no	no	DET
ap-4182	122	5	chiral	chiral	ADJ
ap-4182	122	6	symmetry	symmetry	NOUN
ap-4182	122	7	λ	λ	NOUN
ap-4182	122	8	=	=	PUNCT
ap-4182	123	1	a0σ0	a0σ0	PROPN
ap-4182	123	2	+	+	CCONJ
ap-4182	123	3	a	a	DET
ap-4182	123	4	·	·	PUNCT
ap-4182	123	5	σ	σ	NOUN
ap-4182	123	6	because	because	SCONJ
ap-4182	123	7	a	a	DET
ap-4182	123	8	chiral	chiral	ADJ
ap-4182	123	9	symmetry	symmetry	NOUN
ap-4182	123	10	would	would	AUX
ap-4182	123	11	fulfil	fulfil	VERB
ap-4182	123	12	{	{	PUNCT
ap-4182	123	13	λ	λ	PROPN
ap-4182	123	14	,	,	PUNCT
ap-4182	123	15	h	h	NOUN
ap-4182	123	16	}	}	PUNCT
ap-4182	123	17	=	=	SYM
ap-4182	123	18	3∑	3∑	NUM
ap-4182	123	19	i=0	i=0	PROPN
ap-4182	123	20	3∑	3∑	NUM
ap-4182	123	21	j=1	j=1	PROPN
ap-4182	123	22	ainj{σi	ainj{σi	NOUN
ap-4182	123	23	,	,	PUNCT
ap-4182	123	24	σj	σj	VERB
ap-4182	123	25	}	}	PUNCT
ap-4182	123	26	=	=	SYM
ap-4182	123	27	2	2	NUM
ap-4182	123	28	(	(	PUNCT
ap-4182	123	29	a1n1	a1n1	X
ap-4182	123	30	+	+	CCONJ
ap-4182	123	31	a2n2	a2n2	NOUN
ap-4182	123	32	+	+	PUNCT
ap-4182	123	33	a3n3	a3n3	CCONJ
ap-4182	123	34	)	)	PUNCT
ap-4182	123	35	σ0	σ0	PROPN
ap-4182	124	1	+	+	NUM
ap-4182	124	2	2a0	2a0	NUM
ap-4182	124	3	3∑	3∑	NUM
ap-4182	124	4	j=1	j=1	NOUN
ap-4182	124	5	njσj	njσj	NOUN
ap-4182	124	6	!	!	PUNCT
ap-4182	125	1	=	=	SYM
ap-4182	125	2	0	0	PUNCT
ap-4182	126	1	(	(	PUNCT
ap-4182	126	2	22	22	NUM
ap-4182	126	3	)	)	PUNCT
ap-4182	126	4	with	with	ADP
ap-4182	126	5	a	a	DET
ap-4182	126	6	coefficient	coefficient	NOUN
ap-4182	126	7	vector	vector	NOUN
ap-4182	126	8	a	a	PRON
ap-4182	126	9	which	which	PRON
ap-4182	126	10	is	be	AUX
ap-4182	126	11	independent	independent	ADJ
ap-4182	126	12	of	of	ADP
ap-4182	126	13	the	the	DET
ap-4182	126	14	value	value	NOUN
ap-4182	126	15	of	of	ADP
ap-4182	126	16	k	k	PROPN
ap-4182	126	17	,	,	PUNCT
ap-4182	126	18	the	the	DET
ap-4182	126	19	2×	2×	NUM
ap-4182	126	20	2	2	NUM
ap-4182	126	21	identity	identity	NOUN
ap-4182	126	22	matrix	matrix	NOUN
ap-4182	126	23	σ0	σ0	NOUN
ap-4182	126	24	,	,	PUNCT
ap-4182	126	25	and	and	CCONJ
ap-4182	126	26	the	the	DET
ap-4182	126	27	anti	anti	ADJ
ap-4182	126	28	-	-	ADJ
ap-4182	126	29	commutation	commutation	NOUN
ap-4182	126	30	relations	relation	NOUN
ap-4182	126	31	{	{	PUNCT
ap-4182	126	32	σi	σi	NOUN
ap-4182	126	33	,	,	PUNCT
ap-4182	126	34	σj	σj	VERB
ap-4182	126	35	}	}	PUNCT
ap-4182	126	36	=	=	SYM
ap-4182	126	37	2δijσ0	2δijσ0	NUM
ap-4182	126	38	of	of	ADP
ap-4182	126	39	the	the	DET
ap-4182	126	40	pauli	pauli	PROPN
ap-4182	126	41	matrices	matrix	NOUN
ap-4182	126	42	.	.	PUNCT
ap-4182	127	1	therefore	therefore	ADV
ap-4182	127	2	one	one	NUM
ap-4182	127	3	finds	find	VERB
ap-4182	127	4	a0	a0	NOUN
ap-4182	127	5	=	=	SYM
ap-4182	127	6	0	0	PROPN
ap-4182	127	7	,	,	PUNCT
ap-4182	127	8	and	and	CCONJ
ap-4182	127	9	thus	thus	ADV
ap-4182	127	10	a1n(k)1	a1n(k)1	NUM
ap-4182	127	11	+	+	PUNCT
ap-4182	127	12	a2n(k)2	a2n(k)2	NUM
ap-4182	127	13	+	+	CCONJ
ap-4182	127	14	a3n3	a3n3	ADV
ap-4182	127	15	!	!	PUNCT
ap-4182	128	1	=	=	SYM
ap-4182	128	2	0	0	NUM
ap-4182	128	3	,	,	PUNCT
ap-4182	128	4	(	(	PUNCT
ap-4182	128	5	23	23	NUM
ap-4182	128	6	)	)	PUNCT
ap-4182	128	7	which	which	PRON
ap-4182	128	8	can	can	AUX
ap-4182	128	9	not	not	PART
ap-4182	128	10	be	be	AUX
ap-4182	128	11	satisfied	satisfied	ADJ
ap-4182	128	12	for	for	ADP
ap-4182	128	13	a	a	DET
ap-4182	128	14	constant	constant	ADJ
ap-4182	128	15	vector	vector	NOUN
ap-4182	128	16	a	a	PRON
ap-4182	128	17	because	because	SCONJ
ap-4182	128	18	the	the	DET
ap-4182	128	19	vector	vector	NOUN
ap-4182	128	20	n(k	n(k	PROPN
ap-4182	128	21	)	)	PUNCT
ap-4182	128	22	rotates	rotate	VERB
ap-4182	128	23	on	on	ADP
ap-4182	128	24	a	a	DET
ap-4182	128	25	cylindrical	cylindrical	ADJ
ap-4182	128	26	surface	surface	NOUN
ap-4182	128	27	as	as	SCONJ
ap-4182	128	28	k	k	PROPN
ap-4182	128	29	runs	run	VERB
ap-4182	128	30	through	through	ADP
ap-4182	128	31	the	the	DET
ap-4182	128	32	brillouin	brillouin	NOUN
ap-4182	128	33	zone	zone	NOUN
ap-4182	128	34	.	.	PUNCT
ap-4182	129	1	hence	hence	ADV
ap-4182	129	2	the	the	DET
ap-4182	129	3	nonhermitian	nonhermitian	ADJ
ap-4182	129	4	hamiltonian	hamiltonian	NOUN
ap-4182	129	5	in	in	ADP
ap-4182	129	6	(	(	PUNCT
ap-4182	129	7	18	18	NUM
ap-4182	129	8	)	)	PUNCT
ap-4182	129	9	does	do	AUX
ap-4182	129	10	not	not	PART
ap-4182	129	11	possess	possess	VERB
ap-4182	129	12	a	a	DET
ap-4182	129	13	chiral	chiral	ADJ
ap-4182	129	14	symmetry	symmetry	NOUN
ap-4182	129	15	.	.	PUNCT
ap-4182	130	1	however	however	ADV
ap-4182	130	2	,	,	PUNCT
ap-4182	130	3	this	this	PRON
ap-4182	130	4	does	do	AUX
ap-4182	130	5	not	not	PART
ap-4182	130	6	mean	mean	VERB
ap-4182	130	7	there	there	PRON
ap-4182	130	8	is	be	VERB
ap-4182	130	9	no	no	DET
ap-4182	130	10	quantised	quantised	ADJ
ap-4182	130	11	real	real	ADJ
ap-4182	130	12	part	part	NOUN
ap-4182	130	13	of	of	ADP
ap-4182	130	14	the	the	DET
ap-4182	130	15	zak	zak	PROPN
ap-4182	130	16	phase	phase	NOUN
ap-4182	130	17	since	since	SCONJ
ap-4182	130	18	its	its	PRON
ap-4182	130	19	quantisation	quantisation	NOUN
ap-4182	130	20	is	be	AUX
ap-4182	130	21	ensured	ensure	VERB
ap-4182	130	22	by	by	ADP
ap-4182	130	23	the	the	DET
ap-4182	130	24	argument	argument	NOUN
ap-4182	130	25	of	of	ADP
ap-4182	130	26	hatsugai	hatsugai	PROPN
ap-4182	131	1	[	[	X
ap-4182	131	2	43	43	NUM
ap-4182	131	3	]	]	PUNCT
ap-4182	131	4	in	in	ADP
ap-4182	131	5	the	the	DET
ap-4182	131	6	pt	pt	NOUN
ap-4182	131	7	-unbroken	-unbroken	ADJ
ap-4182	131	8	parameter	parameter	NOUN
ap-4182	131	9	regime	regime	NOUN
ap-4182	131	10	as	as	SCONJ
ap-4182	131	11	mentioned	mention	VERB
ap-4182	131	12	above	above	ADV
ap-4182	131	13	.	.	PUNCT
ap-4182	132	1	at	at	ADP
ap-4182	132	2	the	the	DET
ap-4182	132	3	critical	critical	ADJ
ap-4182	132	4	point	point	NOUN
ap-4182	132	5	γ	γ	X
ap-4182	132	6	=	=	SYM
ap-4182	132	7	0	0	PROPN
ap-4182	132	8	the	the	DET
ap-4182	132	9	system	system	NOUN
ap-4182	132	10	reproduces	reproduce	VERB
ap-4182	132	11	the	the	DET
ap-4182	132	12	hermitian	hermitian	ADJ
ap-4182	132	13	ssh	ssh	NOUN
ap-4182	132	14	model	model	NOUN
ap-4182	132	15	,	,	PUNCT
ap-4182	132	16	which	which	PRON
ap-4182	132	17	possesses	possess	VERB
ap-4182	132	18	the	the	DET
ap-4182	132	19	previously	previously	ADV
ap-4182	132	20	mentioned	mention	VERB
ap-4182	132	21	symmetries	symmetry	NOUN
ap-4182	132	22	.	.	PUNCT
ap-4182	133	1	for	for	ADP
ap-4182	133	2	γ	γ	X
ap-4182	133	3	<	<	X
ap-4182	133	4	0	0	NUM
ap-4182	133	5	the	the	DET
ap-4182	133	6	particle	particle	NOUN
ap-4182	133	7	sinks	sink	NOUN
ap-4182	133	8	and	and	CCONJ
ap-4182	133	9	sources	source	NOUN
ap-4182	133	10	are	be	AUX
ap-4182	133	11	interchanged	interchange	VERB
ap-4182	133	12	leading	lead	VERB
ap-4182	133	13	to	to	ADP
ap-4182	133	14	a	a	DET
ap-4182	133	15	spatially	spatially	ADV
ap-4182	133	16	reflected	reflect	VERB
ap-4182	133	17	system	system	NOUN
ap-4182	133	18	with	with	ADP
ap-4182	133	19	the	the	DET
ap-4182	133	20	same	same	ADJ
ap-4182	133	21	general	general	ADJ
ap-4182	133	22	properties	property	NOUN
ap-4182	133	23	as	as	ADP
ap-4182	133	24	the	the	DET
ap-4182	133	25	system	system	NOUN
ap-4182	133	26	with	with	ADP
ap-4182	133	27	γ	γ	X
ap-4182	133	28	>	>	X
ap-4182	133	29	0	0	NUM
ap-4182	133	30	.	.	PUNCT
ap-4182	134	1	from	from	ADP
ap-4182	134	2	the	the	DET
ap-4182	134	3	bloch	bloch	PROPN
ap-4182	134	4	hamiltonian	hamiltonian	NOUN
ap-4182	134	5	(	(	PUNCT
ap-4182	134	6	cf	cf	NOUN
ap-4182	134	7	.	.	PUNCT
ap-4182	135	1	(	(	PUNCT
ap-4182	135	2	18	18	NUM
ap-4182	135	3	)	)	PUNCT
ap-4182	135	4	)	)	PUNCT
ap-4182	136	1	the	the	DET
ap-4182	136	2	complex	complex	ADJ
ap-4182	136	3	zak	zak	PROPN
ap-4182	136	4	phase	phase	NOUN
ap-4182	136	5	can	can	AUX
ap-4182	136	6	be	be	AUX
ap-4182	136	7	calculated	calculate	VERB
ap-4182	136	8	following	follow	VERB
ap-4182	136	9	the	the	DET
ap-4182	136	10	steps	step	NOUN
ap-4182	136	11	explained	explain	VERB
ap-4182	136	12	in	in	ADP
ap-4182	136	13	section	section	NOUN
ap-4182	136	14	3	3	NUM
ap-4182	136	15	.	.	PUNCT
ap-4182	137	1	we	we	PRON
ap-4182	137	2	choose	choose	VERB
ap-4182	137	3	(	(	PUNCT
ap-4182	137	4	cf	cf	NOUN
ap-4182	137	5	.	.	PUNCT
ap-4182	137	6	(	(	PUNCT
ap-4182	137	7	11a	11a	NUM
ap-4182	137	8	)	)	PUNCT
ap-4182	137	9	)	)	PUNCT
ap-4182	137	10	f∆ϕn	f∆ϕn	NOUN
ap-4182	137	11	(	(	PUNCT
ap-4182	137	12	x	x	NOUN
ap-4182	137	13	)	)	PUNCT
ap-4182	137	14	=	=	SYM
ap-4182	137	15	∆ϕnx−	∆ϕnx−	NOUN
ap-4182	137	16	2π	2π	NOUN
ap-4182	137	17	with	with	ADP
ap-4182	137	18	x	x	X
ap-4182	137	19	=	=	SYM
ap-4182	137	20	k	k	PROPN
ap-4182	138	1	+	+	NUM
ap-4182	138	2	π	π	X
ap-4182	138	3	/	/	X
ap-4182	138	4	a	a	DET
ap-4182	138	5	2π	2π	NOUN
ap-4182	138	6	/	/	SYM
ap-4182	138	7	a	a	PRON
ap-4182	138	8	,	,	PUNCT
ap-4182	138	9	(	(	PUNCT
ap-4182	138	10	24	24	NUM
ap-4182	138	11	)	)	PUNCT
ap-4182	138	12	which	which	PRON
ap-4182	138	13	is	be	AUX
ap-4182	138	14	the	the	DET
ap-4182	138	15	most	most	ADV
ap-4182	138	16	simple	simple	ADJ
ap-4182	138	17	function	function	NOUN
ap-4182	138	18	fulfilling	fulfil	VERB
ap-4182	138	19	the	the	DET
ap-4182	138	20	conditions	condition	NOUN
ap-4182	138	21	(	(	PUNCT
ap-4182	138	22	11b	11b	NOUN
ap-4182	138	23	)	)	PUNCT
ap-4182	138	24	.	.	PUNCT
ap-4182	139	1	figure	figure	NOUN
ap-4182	139	2	2	2	NUM
ap-4182	139	3	illustrates	illustrate	VERB
ap-4182	139	4	the	the	DET
ap-4182	139	5	gauge	gauge	NOUN
ap-4182	139	6	smoothing	smoothing	NOUN
ap-4182	139	7	process	process	NOUN
ap-4182	139	8	using	use	VERB
ap-4182	139	9	the	the	DET
ap-4182	139	10	first	first	ADJ
ap-4182	139	11	non	non	ADJ
ap-4182	139	12	-	-	ADJ
ap-4182	139	13	vanishing	vanishing	ADJ
ap-4182	139	14	component	component	NOUN
ap-4182	139	15	p	p	NOUN
ap-4182	139	16	=	=	NOUN
ap-4182	139	17	1	1	NUM
ap-4182	139	18	of	of	ADP
ap-4182	139	19	the	the	DET
ap-4182	139	20	left	left	ADJ
ap-4182	139	21	basis	basis	NOUN
ap-4182	139	22	states	state	NOUN
ap-4182	139	23	as	as	ADP
ap-4182	139	24	an	an	DET
ap-4182	139	25	example	example	NOUN
ap-4182	139	26	.	.	PUNCT
ap-4182	140	1	the	the	DET
ap-4182	140	2	component	component	NOUN
ap-4182	140	3	〈	〈	PROPN
ap-4182	140	4	χ1(αj)|1	χ1(αj)|1	NOUN
ap-4182	140	5	of	of	ADP
ap-4182	140	6	the	the	DET
ap-4182	140	7	unnormalised	unnormalised	ADJ
ap-4182	140	8	left	left	NOUN
ap-4182	140	9	eigenvector	eigenvector	NOUN
ap-4182	140	10	is	be	AUX
ap-4182	140	11	shown	show	VERB
ap-4182	140	12	in	in	ADP
ap-4182	140	13	figure	figure	NOUN
ap-4182	140	14	2	2	NUM
ap-4182	140	15	(	(	PUNCT
ap-4182	140	16	a	a	NOUN
ap-4182	140	17	)	)	PUNCT
ap-4182	140	18	.	.	PUNCT
ap-4182	141	1	one	one	PRON
ap-4182	141	2	can	can	AUX
ap-4182	141	3	see	see	VERB
ap-4182	141	4	two	two	NUM
ap-4182	141	5	different	different	ADJ
ap-4182	141	6	phase	phase	NOUN
ap-4182	141	7	branches	branch	NOUN
ap-4182	141	8	as	as	ADP
ap-4182	141	9	a	a	DET
ap-4182	141	10	result	result	NOUN
ap-4182	141	11	of	of	ADP
ap-4182	141	12	the	the	DET
ap-4182	141	13	numerical	numerical	ADJ
ap-4182	141	14	diagonalisation	diagonalisation	NOUN
ap-4182	141	15	and	and	CCONJ
ap-4182	141	16	a	a	DET
ap-4182	141	17	constant	constant	ADJ
ap-4182	141	18	modulus	modulus	NOUN
ap-4182	141	19	.	.	PUNCT
ap-4182	142	1	after	after	SCONJ
ap-4182	142	2	the	the	DET
ap-4182	142	3	gauge	gauge	NOUN
ap-4182	142	4	smoothing	smoothing	NOUN
ap-4182	142	5	and	and	CCONJ
ap-4182	142	6	normalisation	normalisation	NOUN
ap-4182	142	7	according	accord	VERB
ap-4182	142	8	to	to	ADP
ap-4182	142	9	the	the	DET
ap-4182	142	10	first	first	ADJ
ap-4182	142	11	step	step	NOUN
ap-4182	142	12	described	describe	VERB
ap-4182	142	13	in	in	ADP
ap-4182	142	14	section	section	NOUN
ap-4182	142	15	3	3	NUM
ap-4182	142	16	as	as	SCONJ
ap-4182	142	17	shown	show	VERB
ap-4182	142	18	in	in	ADP
ap-4182	142	19	figure	figure	NOUN
ap-4182	142	20	2	2	NUM
ap-4182	142	21	(	(	PUNCT
ap-4182	142	22	b	b	NOUN
ap-4182	142	23	)	)	PUNCT
ap-4182	142	24	the	the	DET
ap-4182	142	25	modulus	modulus	NOUN
ap-4182	142	26	varies	vary	VERB
ap-4182	142	27	with	with	ADP
ap-4182	142	28	the	the	DET
ap-4182	142	29	wave	wave	NOUN
ap-4182	142	30	number	number	NOUN
ap-4182	142	31	k	k	PROPN
ap-4182	143	1	and	and	CCONJ
ap-4182	143	2	there	there	PRON
ap-4182	143	3	is	be	VERB
ap-4182	143	4	only	only	ADV
ap-4182	143	5	one	one	NUM
ap-4182	143	6	phase	phase	NOUN
ap-4182	143	7	branch	branch	NOUN
ap-4182	143	8	left	leave	VERB
ap-4182	143	9	,	,	PUNCT
ap-4182	143	10	but	but	CCONJ
ap-4182	143	11	the	the	DET
ap-4182	143	12	basis	basis	NOUN
ap-4182	143	13	is	be	AUX
ap-4182	143	14	not	not	PART
ap-4182	143	15	yet	yet	ADV
ap-4182	143	16	single	single	ADV
ap-4182	143	17	-	-	PUNCT
ap-4182	143	18	valued	value	VERB
ap-4182	143	19	as	as	SCONJ
ap-4182	143	20	there	there	PRON
ap-4182	143	21	is	be	VERB
ap-4182	143	22	still	still	ADV
ap-4182	143	23	a	a	DET
ap-4182	143	24	phase	phase	NOUN
ap-4182	143	25	difference	difference	NOUN
ap-4182	143	26	at	at	ADP
ap-4182	143	27	the	the	DET
ap-4182	143	28	boundaries	boundary	NOUN
ap-4182	143	29	of	of	ADP
ap-4182	143	30	the	the	DET
ap-4182	143	31	brillouin	brillouin	NOUN
ap-4182	143	32	zone	zone	NOUN
ap-4182	143	33	.	.	PUNCT
ap-4182	144	1	in	in	ADP
ap-4182	144	2	this	this	DET
ap-4182	144	3	example	example	NOUN
ap-4182	144	4	the	the	DET
ap-4182	144	5	factor	factor	NOUN
ap-4182	144	6	x	x	PUNCT
ap-4182	145	1	=	=	PUNCT
ap-4182	145	2	−1	−1	NOUN
ap-4182	145	3	has	have	VERB
ap-4182	145	4	to	to	PART
ap-4182	145	5	be	be	AUX
ap-4182	145	6	used	use	VERB
ap-4182	145	7	as	as	ADP
ap-4182	145	8	ϕ1,j	ϕ1,j	PROPN
ap-4182	145	9	jumps	jump	VERB
ap-4182	145	10	from	from	ADP
ap-4182	145	11	−π	−π	NUM
ap-4182	145	12	to	to	ADP
ap-4182	145	13	π	π	PROPN
ap-4182	145	14	.	.	PUNCT
ap-4182	146	1	after	after	ADP
ap-4182	146	2	the	the	DET
ap-4182	146	3	second	second	ADJ
ap-4182	146	4	step	step	NOUN
ap-4182	146	5	the	the	DET
ap-4182	146	6	component	component	NOUN
ap-4182	146	7	〈	〈	PROPN
ap-4182	146	8	χ1(αj)|1	χ1(αj)|1	NOUN
ap-4182	146	9	of	of	ADP
ap-4182	146	10	the	the	DET
ap-4182	146	11	final	final	ADJ
ap-4182	146	12	left	left	ADJ
ap-4182	146	13	eigenvector	eigenvector	NOUN
ap-4182	146	14	is	be	AUX
ap-4182	146	15	the	the	DET
ap-4182	146	16	same	same	ADJ
ap-4182	146	17	at	at	ADP
ap-4182	146	18	the	the	DET
ap-4182	146	19	brillouin	brillouin	NOUN
ap-4182	146	20	zone	zone	NOUN
ap-4182	146	21	boundaries	boundary	NOUN
ap-4182	146	22	in	in	ADP
ap-4182	146	23	figure	figure	NOUN
ap-4182	146	24	2	2	NUM
ap-4182	146	25	(	(	PUNCT
ap-4182	146	26	c	c	NOUN
ap-4182	146	27	)	)	PUNCT
ap-4182	146	28	.	.	PUNCT
ap-4182	147	1	the	the	DET
ap-4182	147	2	two	two	NUM
ap-4182	147	3	complex	complex	ADJ
ap-4182	147	4	zak	zak	PROPN
ap-4182	147	5	phases	phase	NOUN
ap-4182	147	6	γ1	γ1	PROPN
ap-4182	147	7	and	and	CCONJ
ap-4182	147	8	γ2	γ2	PROPN
ap-4182	147	9	following	follow	VERB
ap-4182	147	10	from	from	ADP
ap-4182	147	11	the	the	DET
ap-4182	147	12	eigenvector	eigenvector	NOUN
ap-4182	147	13	pairs	pair	NOUN
ap-4182	147	14	of	of	ADP
ap-4182	147	15	h(k	h(k	PROPN
ap-4182	147	16	)	)	PUNCT
ap-4182	147	17	are	be	AUX
ap-4182	147	18	shown	show	VERB
ap-4182	147	19	in	in	ADP
ap-4182	147	20	figures	figure	NOUN
ap-4182	147	21	3	3	NUM
ap-4182	147	22	(	(	PUNCT
ap-4182	147	23	a	a	NOUN
ap-4182	147	24	)	)	PUNCT
ap-4182	147	25	and	and	CCONJ
ap-4182	147	26	(	(	PUNCT
ap-4182	147	27	b	b	NOUN
ap-4182	147	28	)	)	PUNCT
ap-4182	147	29	,	,	PUNCT
ap-4182	147	30	where	where	SCONJ
ap-4182	147	31	the	the	DET
ap-4182	147	32	control	control	NOUN
ap-4182	147	33	parameter	parameter	NOUN
ap-4182	147	34	θ	θ	PROPN
ap-4182	147	35	is	be	AUX
ap-4182	147	36	used	use	VERB
ap-4182	147	37	to	to	PART
ap-4182	147	38	describe	describe	VERB
ap-4182	147	39	the	the	DET
ap-4182	147	40	difference	difference	NOUN
ap-4182	147	41	between	between	ADP
ap-4182	147	42	the	the	DET
ap-4182	147	43	two	two	NUM
ap-4182	147	44	tunnelling	tunnelling	NOUN
ap-4182	147	45	amplitudes	amplitude	NOUN
ap-4182	147	46	t+	t+	NUM
ap-4182	147	47	and	and	CCONJ
ap-4182	147	48	t−	t−	NOUN
ap-4182	147	49	,	,	PUNCT
ap-4182	147	50	t±	t±	ADP
ap-4182	147	51	=	=	SYM
ap-4182	147	52	t	t	PROPN
ap-4182	147	53	(	(	PUNCT
ap-4182	147	54	1±∆cos(θ	1±∆cos(θ	NUM
ap-4182	147	55	)	)	PUNCT
ap-4182	147	56	)	)	PUNCT
ap-4182	148	1	(	(	PUNCT
ap-4182	148	2	25	25	NUM
ap-4182	148	3	)	)	PUNCT
ap-4182	148	4	with	with	ADP
ap-4182	148	5	the	the	DET
ap-4182	148	6	mean	mean	ADJ
ap-4182	148	7	value	value	NOUN
ap-4182	148	8	of	of	ADP
ap-4182	148	9	the	the	DET
ap-4182	148	10	tunnelling	tunnelling	NOUN
ap-4182	148	11	amplitude	amplitude	NOUN
ap-4182	148	12	t	t	NOUN
ap-4182	148	13	and	and	CCONJ
ap-4182	148	14	the	the	DET
ap-4182	148	15	dimerization	dimerization	NOUN
ap-4182	148	16	strength	strength	NOUN
ap-4182	148	17	∆.	∆.	PUNCT
ap-4182	148	18	to	to	PART
ap-4182	148	19	verify	verify	VERB
ap-4182	148	20	our	our	PRON
ap-4182	148	21	results	result	NOUN
ap-4182	148	22	we	we	PRON
ap-4182	148	23	compare	compare	VERB
ap-4182	148	24	them	they	PRON
ap-4182	148	25	with	with	ADP
ap-4182	148	26	the	the	DET
ap-4182	148	27	analytical	analytical	ADJ
ap-4182	148	28	ones	one	NOUN
ap-4182	148	29	derived	derive	VERB
ap-4182	148	30	in	in	ADP
ap-4182	148	31	[	[	X
ap-4182	148	32	37	37	NUM
ap-4182	148	33	]	]	PUNCT
ap-4182	148	34	,	,	PUNCT
ap-4182	148	35	γ1/2	γ1/2	PROPN
ap-4182	148	36	=	=	PRON
ap-4182	148	37	πθ(q	πθ(q	X
ap-4182	148	38	−	−	PROPN
ap-4182	148	39	1)±	1)±	NUM
ap-4182	149	1	iη2	iη2	NOUN
ap-4182	149	2	√	√	ADP
ap-4182	149	3	ν	ν	X
ap-4182	149	4	q	q	X
ap-4182	149	5	(	(	PUNCT
ap-4182	149	6	k(ν	k(ν	PROPN
ap-4182	149	7	)	)	PUNCT
ap-4182	150	1	+	+	CCONJ
ap-4182	150	2	q	q	NOUN
ap-4182	150	3	−	−	PROPN
ap-4182	150	4	1	1	NUM
ap-4182	150	5	q	q	NOUN
ap-4182	150	6	+	+	NUM
ap-4182	150	7	1π(µ	1π(µ	NUM
ap-4182	150	8	,	,	PUNCT
ap-4182	150	9	ν	ν	NOUN
ap-4182	150	10	)	)	PUNCT
ap-4182	150	11	)	)	PUNCT
ap-4182	150	12	,	,	PUNCT
ap-4182	150	13	(	(	PUNCT
ap-4182	150	14	26	26	NUM
ap-4182	150	15	)	)	PUNCT
ap-4182	150	16	473	473	NUM
ap-4182	150	17	m.	m.	NOUN
ap-4182	150	18	wagner	wagner	PROPN
ap-4182	150	19	,	,	PUNCT
ap-4182	150	20	f.	f.	PROPN
ap-4182	150	21	dangel	dangel	PROPN
ap-4182	150	22	,	,	PUNCT
ap-4182	150	23	h.	h.	PROPN
ap-4182	150	24	cartarius	cartarius	PROPN
ap-4182	150	25	et	et	PROPN
ap-4182	150	26	al	al	PROPN
ap-4182	150	27	.	.	PROPN
ap-4182	150	28	acta	acta	PROPN
ap-4182	150	29	polytechnica	polytechnica	PROPN
ap-4182	151	1	−π	−π	ADV
ap-4182	151	2	0	0	PUNCT
ap-4182	152	1	π	π	NOUN
ap-4182	152	2	0	0	NUM
ap-4182	152	3	1	1	NUM
ap-4182	152	4	2(a	2(a	NUM
ap-4182	152	5	)	)	PUNCT
ap-4182	152	6	−π	−π	ADV
ap-4182	152	7	0	0	NUM
ap-4182	153	1	π	π	NOUN
ap-4182	153	2	0	0	NUM
ap-4182	153	3	1	1	NUM
ap-4182	153	4	2	2	NUM
ap-4182	153	5	}	}	PUNCT
ap-4182	153	6	=	=	SYM
ap-4182	153	7	∆ϕ̃1	∆ϕ̃1	PROPN
ap-4182	153	8	(	(	PUNCT
ap-4182	153	9	b	b	NOUN
ap-4182	153	10	)	)	PUNCT
ap-4182	153	11	ϕ	ϕ	NOUN
ap-4182	153	12	1	1	NUM
ap-4182	153	13	,	,	PUNCT
ap-4182	153	14	j	j	PROPN
ap-4182	153	15	∣	∣	ADJ
ap-4182	153	16	∣	∣	PROPN
ap-4182	153	17	〈	〈	PROPN
ap-4182	153	18	χ	χ	ADP
ap-4182	153	19	1	1	NUM
ap-4182	153	20	(	(	PUNCT
ap-4182	153	21	α	α	NOUN
ap-4182	153	22	j	j	PROPN
ap-4182	153	23	)	)	PUNCT
ap-4182	153	24	|	|	ADV
ap-4182	153	25	1	1	NUM
ap-4182	153	26	∣	∣	PROPN
ap-4182	153	27	∣	∣	ADJ
ap-4182	153	28	−π	−π	NUM
ap-4182	153	29	0	0	NUM
ap-4182	153	30	π	π	X
ap-4182	153	31	−1	−1	NOUN
ap-4182	153	32	−0.5	−0.5	NOUN
ap-4182	153	33	0	0	NUM
ap-4182	153	34	0.5	0.5	NUM
ap-4182	153	35	1	1	NUM
ap-4182	153	36	0	0	NUM
ap-4182	153	37	1	1	NUM
ap-4182	153	38	2	2	NUM
ap-4182	153	39	k	k	NOUN
ap-4182	153	40	/	/	SYM
ap-4182	153	41	π∣∣〈χ1(αj)|1	π∣∣〈χ1(αj)|1	NOUN
ap-4182	153	42	∣∣ϕ1,j	∣∣ϕ1,j	NOUN
ap-4182	153	43	(	(	PUNCT
ap-4182	153	44	c	c	NOUN
ap-4182	153	45	)	)	PUNCT
ap-4182	153	46	figure	figure	NOUN
ap-4182	153	47	2	2	NUM
ap-4182	153	48	.	.	PUNCT
ap-4182	154	1	(	(	PUNCT
ap-4182	154	2	colour	colour	NOUN
ap-4182	154	3	online	online	NOUN
ap-4182	154	4	)	)	PUNCT
ap-4182	155	1	first	first	ADJ
ap-4182	155	2	component	component	NOUN
ap-4182	155	3	of	of	ADP
ap-4182	155	4	the	the	DET
ap-4182	155	5	left	left	ADJ
ap-4182	155	6	handed	hand	VERB
ap-4182	155	7	eigenvector	eigenvector	NOUN
ap-4182	155	8	〈	〈	PROPN
ap-4182	155	9	χ1(αj)|1	χ1(αj)|1	NOUN
ap-4182	155	10	in	in	ADP
ap-4182	155	11	dependence	dependence	NOUN
ap-4182	155	12	of	of	ADP
ap-4182	155	13	the	the	DET
ap-4182	155	14	wave	wave	NOUN
ap-4182	155	15	number	number	NOUN
ap-4182	155	16	k	k	PROPN
ap-4182	155	17	with	with	ADP
ap-4182	155	18	t	t	PROPN
ap-4182	155	19	=	=	SYM
ap-4182	155	20	1	1	NUM
ap-4182	155	21	,	,	PUNCT
ap-4182	155	22	∆	∆	PROPN
ap-4182	155	23	=	=	SYM
ap-4182	155	24	1/2	1/2	NUM
ap-4182	155	25	,	,	PUNCT
ap-4182	155	26	γ	γ	NOUN
ap-4182	155	27	=	=	SYM
ap-4182	155	28	1	1	NUM
ap-4182	155	29	and	and	CCONJ
ap-4182	155	30	θ	θ	PROPN
ap-4182	156	1	≈	≈	NOUN
ap-4182	156	2	0.3π	0.3π	NUM
ap-4182	156	3	:	:	PUNCT
ap-4182	156	4	(	(	PUNCT
ap-4182	156	5	a	a	X
ap-4182	156	6	)	)	PUNCT
ap-4182	156	7	before	before	ADP
ap-4182	156	8	the	the	DET
ap-4182	156	9	steps	step	NOUN
ap-4182	156	10	described	describe	VERB
ap-4182	156	11	in	in	ADP
ap-4182	156	12	(	(	PUNCT
ap-4182	156	13	6a	6a	NOUN
ap-4182	156	14	)	)	PUNCT
ap-4182	156	15	and	and	CCONJ
ap-4182	156	16	(	(	PUNCT
ap-4182	156	17	6b	6b	NOUN
ap-4182	156	18	)	)	PUNCT
ap-4182	156	19	one	one	PRON
ap-4182	156	20	can	can	AUX
ap-4182	156	21	identify	identify	VERB
ap-4182	156	22	two	two	NUM
ap-4182	156	23	different	different	ADJ
ap-4182	156	24	phase	phase	NOUN
ap-4182	156	25	branches	branch	NOUN
ap-4182	156	26	(	(	PUNCT
ap-4182	156	27	blue	blue	ADJ
ap-4182	156	28	line	line	NOUN
ap-4182	156	29	)	)	PUNCT
ap-4182	156	30	and	and	CCONJ
ap-4182	156	31	a	a	DET
ap-4182	156	32	constant	constant	ADJ
ap-4182	156	33	modulus	modulus	NOUN
ap-4182	156	34	(	(	PUNCT
ap-4182	156	35	filled	fill	VERB
ap-4182	156	36	red	red	ADJ
ap-4182	156	37	dots	dot	NOUN
ap-4182	156	38	)	)	PUNCT
ap-4182	156	39	.	.	PUNCT
ap-4182	157	1	(	(	PUNCT
ap-4182	157	2	b	b	X
ap-4182	157	3	)	)	PUNCT
ap-4182	157	4	after	after	ADP
ap-4182	157	5	the	the	DET
ap-4182	157	6	steps	step	NOUN
ap-4182	157	7	characterised	characterise	VERB
ap-4182	157	8	by	by	ADP
ap-4182	157	9	(	(	PUNCT
ap-4182	157	10	4a	4a	NUM
ap-4182	157	11	)	)	PUNCT
ap-4182	157	12	and	and	CCONJ
ap-4182	157	13	(	(	PUNCT
ap-4182	157	14	4b	4b	X
ap-4182	157	15	)	)	PUNCT
ap-4182	157	16	(	(	PUNCT
ap-4182	157	17	here	here	ADV
ap-4182	157	18	∆ϕ̃1	∆ϕ̃1	PROPN
ap-4182	157	19	=	=	PUNCT
ap-4182	157	20	ϕm,1	ϕm,1	PROPN
ap-4182	157	21	−	−	PROPN
ap-4182	158	1	ϕ1,1	ϕ1,1	INTJ
ap-4182	159	1	and	and	CCONJ
ap-4182	159	2	x	x	X
ap-4182	159	3	=	=	SYM
ap-4182	159	4	−1	−1	NOUN
ap-4182	159	5	cf	cf	NOUN
ap-4182	159	6	.	.	PUNCT
ap-4182	160	1	(	(	PUNCT
ap-4182	160	2	9	9	NUM
ap-4182	160	3	)	)	PUNCT
ap-4182	160	4	)	)	PUNCT
ap-4182	161	1	the	the	DET
ap-4182	161	2	phase	phase	NOUN
ap-4182	161	3	is	be	AUX
ap-4182	161	4	smooth	smooth	ADJ
ap-4182	161	5	within	within	ADP
ap-4182	161	6	the	the	DET
ap-4182	161	7	brillouin	brillouin	NOUN
ap-4182	161	8	zone	zone	NOUN
ap-4182	161	9	but	but	CCONJ
ap-4182	161	10	discontinuous	discontinuous	ADJ
ap-4182	161	11	at	at	ADP
ap-4182	161	12	its	its	PRON
ap-4182	161	13	boundaries	boundary	NOUN
ap-4182	161	14	,	,	PUNCT
ap-4182	161	15	and	and	CCONJ
ap-4182	161	16	the	the	DET
ap-4182	161	17	modulus	modulus	NOUN
ap-4182	161	18	varies	vary	VERB
ap-4182	161	19	with	with	ADP
ap-4182	161	20	k.	k.	PROPN
ap-4182	161	21	(	(	PUNCT
ap-4182	161	22	c	c	X
ap-4182	161	23	)	)	PUNCT
ap-4182	161	24	after	after	ADP
ap-4182	161	25	the	the	DET
ap-4182	161	26	gauge	gauge	NOUN
ap-4182	161	27	smoothing	smoothing	NOUN
ap-4182	161	28	process	process	NOUN
ap-4182	161	29	the	the	DET
ap-4182	161	30	phase	phase	NOUN
ap-4182	161	31	difference	difference	NOUN
ap-4182	161	32	∆ϕ̃1	∆ϕ̃1	PROPN
ap-4182	161	33	is	be	AUX
ap-4182	161	34	compensated	compensate	VERB
ap-4182	161	35	and	and	CCONJ
ap-4182	161	36	the	the	DET
ap-4182	161	37	phase	phase	NOUN
ap-4182	161	38	is	be	AUX
ap-4182	161	39	continuous	continuous	ADJ
ap-4182	161	40	and	and	CCONJ
ap-4182	161	41	smooth	smooth	ADJ
ap-4182	161	42	in	in	ADP
ap-4182	161	43	the	the	DET
ap-4182	161	44	whole	whole	ADJ
ap-4182	161	45	brillouin	brillouin	NOUN
ap-4182	161	46	zone	zone	NOUN
ap-4182	161	47	.	.	PUNCT
ap-4182	162	1	where	where	SCONJ
ap-4182	162	2	q	q	NOUN
ap-4182	162	3	=	=	NOUN
ap-4182	162	4	t+/t−	t+/t−	X
ap-4182	162	5	is	be	AUX
ap-4182	162	6	the	the	DET
ap-4182	162	7	ratio	ratio	NOUN
ap-4182	162	8	of	of	ADP
ap-4182	162	9	the	the	DET
ap-4182	162	10	tunnelling	tunnelling	NOUN
ap-4182	162	11	amplitudes	amplitude	NOUN
ap-4182	162	12	,	,	PUNCT
ap-4182	162	13	η	η	NOUN
ap-4182	162	14	=	=	SYM
ap-4182	162	15	γ/(2t−	γ/(2t−	PROPN
ap-4182	162	16	)	)	PUNCT
ap-4182	162	17	and	and	CCONJ
ap-4182	162	18	ν	ν	X
ap-4182	162	19	=	=	SYM
ap-4182	162	20	4q/((q	4q/((q	NUM
ap-4182	163	1	+	+	CCONJ
ap-4182	163	2	1)2	1)2	NUM
ap-4182	163	3	−	−	NOUN
ap-4182	163	4	η2	η2	PROPN
ap-4182	163	5	)	)	PUNCT
ap-4182	163	6	and	and	CCONJ
ap-4182	163	7	µ	µ	X
ap-4182	163	8	=	=	SYM
ap-4182	163	9	4q/(q	4q/(q	NUM
ap-4182	163	10	+	+	CCONJ
ap-4182	163	11	1)2	1)2	NUM
ap-4182	163	12	.	.	PUNCT
ap-4182	164	1	k(ν	k(ν	PROPN
ap-4182	164	2	)	)	PUNCT
ap-4182	165	1	and	and	CCONJ
ap-4182	165	2	π(µ	π(µ	ADV
ap-4182	165	3	,	,	PUNCT
ap-4182	165	4	ν	ν	X
ap-4182	165	5	)	)	PUNCT
ap-4182	165	6	are	be	AUX
ap-4182	165	7	elliptic	elliptic	ADJ
ap-4182	165	8	integrals	integral	NOUN
ap-4182	165	9	of	of	ADP
ap-4182	165	10	first	first	ADJ
ap-4182	165	11	and	and	CCONJ
ap-4182	165	12	third	third	ADJ
ap-4182	165	13	kind	kind	NOUN
ap-4182	165	14	,	,	PUNCT
ap-4182	165	15	k(ν	k(ν	PROPN
ap-4182	165	16	)	)	PUNCT
ap-4182	166	1	=	=	SYM
ap-4182	166	2	π/2∫	π/2∫	NOUN
ap-4182	166	3	0	0	NUM
ap-4182	166	4	dk√	dk√	NOUN
ap-4182	166	5	1−	1−	NUM
ap-4182	166	6	ν	ν	X
ap-4182	166	7	sin2(k	sin2(k	NOUN
ap-4182	166	8	)	)	PUNCT
ap-4182	166	9	,	,	PUNCT
ap-4182	166	10	(	(	PUNCT
ap-4182	166	11	27	27	NUM
ap-4182	166	12	)	)	PUNCT
ap-4182	166	13	π(µ	π(µ	ADV
ap-4182	166	14	,	,	PUNCT
ap-4182	166	15	ν	ν	X
ap-4182	166	16	)	)	PUNCT
ap-4182	167	1	=	=	SYM
ap-4182	167	2	π/2∫	π/2∫	NOUN
ap-4182	167	3	0	0	NUM
ap-4182	168	1	dk	dk	PROPN
ap-4182	168	2	1−	1−	NUM
ap-4182	168	3	µ	µ	X
ap-4182	168	4	sin2(k	sin2(k	NOUN
ap-4182	168	5	)	)	PUNCT
ap-4182	168	6	√	√	NOUN
ap-4182	168	7	1−	1−	NUM
ap-4182	168	8	ν	ν	X
ap-4182	168	9	sin2(k	sin2(k	NOUN
ap-4182	168	10	)	)	PUNCT
ap-4182	168	11	.	.	PUNCT
ap-4182	169	1	(	(	PUNCT
ap-4182	169	2	28	28	NUM
ap-4182	169	3	)	)	PUNCT
ap-4182	169	4	the	the	DET
ap-4182	169	5	numerical	numerical	PROPN
ap-4182	169	6	calculations	calculation	NOUN
ap-4182	169	7	perfectly	perfectly	ADV
ap-4182	169	8	reproduce	reproduce	VERB
ap-4182	169	9	the	the	DET
ap-4182	169	10	analytical	analytical	ADJ
ap-4182	169	11	results	result	NOUN
ap-4182	169	12	.	.	PUNCT
ap-4182	170	1	the	the	DET
ap-4182	170	2	grey	grey	PROPN
ap-4182	170	3	shaded	shade	VERB
ap-4182	170	4	areas	area	NOUN
ap-4182	170	5	in	in	ADP
ap-4182	170	6	figure	figure	NOUN
ap-4182	170	7	3	3	NUM
ap-4182	170	8	mark	mark	VERB
ap-4182	170	9	the	the	DET
ap-4182	170	10	values	value	NOUN
ap-4182	170	11	of	of	ADP
ap-4182	170	12	θ	θ	PROPN
ap-4182	170	13	for	for	ADP
ap-4182	170	14	which	which	PRON
ap-4182	170	15	the	the	DET
ap-4182	170	16	system	system	NOUN
ap-4182	170	17	is	be	AUX
ap-4182	170	18	in	in	ADP
ap-4182	170	19	a	a	DET
ap-4182	170	20	pt	pt	NOUN
ap-4182	170	21	broken	break	VERB
ap-4182	170	22	phase	phase	NOUN
ap-4182	170	23	,	,	PUNCT
ap-4182	170	24	for	for	ADP
ap-4182	170	25	all	all	DET
ap-4182	170	26	other	other	ADJ
ap-4182	170	27	values	value	NOUN
ap-4182	170	28	of	of	ADP
ap-4182	170	29	θ	θ	NOUN
ap-4182	170	30	the	the	DET
ap-4182	170	31	system	system	NOUN
ap-4182	170	32	is	be	AUX
ap-4182	170	33	in	in	ADP
ap-4182	170	34	a	a	DET
ap-4182	170	35	pt	pt	X
ap-4182	170	36	-unbroken	-unbroken	ADJ
ap-4182	170	37	phase	phase	NOUN
ap-4182	170	38	.	.	PUNCT
ap-4182	171	1	in	in	ADP
ap-4182	171	2	the	the	DET
ap-4182	171	3	pt	pt	NOUN
ap-4182	171	4	-symmetric	-symmetric	ADJ
ap-4182	171	5	regime	regime	NOUN
ap-4182	171	6	the	the	DET
ap-4182	171	7	real	real	ADJ
ap-4182	171	8	part	part	NOUN
ap-4182	171	9	of	of	ADP
ap-4182	171	10	the	the	DET
ap-4182	171	11	complex	complex	ADJ
ap-4182	171	12	zak	zak	PROPN
ap-4182	171	13	phase	phase	NOUN
ap-4182	171	14	is	be	AUX
ap-4182	171	15	either	either	CCONJ
ap-4182	171	16	0	0	NUM
ap-4182	171	17	or	or	CCONJ
ap-4182	171	18	π	π	PROPN
ap-4182	171	19	modulo	modulo	VERB
ap-4182	171	20	2π	2π	NOUN
ap-4182	171	21	and	and	CCONJ
ap-4182	171	22	can	can	AUX
ap-4182	171	23	be	be	AUX
ap-4182	171	24	used	use	VERB
ap-4182	171	25	to	to	PART
ap-4182	171	26	characterise	characterise	VERB
ap-4182	171	27	the	the	DET
ap-4182	171	28	topological	topological	ADJ
ap-4182	171	29	phase	phase	NOUN
ap-4182	171	30	of	of	ADP
ap-4182	171	31	the	the	DET
ap-4182	171	32	system	system	NOUN
ap-4182	171	33	.	.	PUNCT
ap-4182	172	1	5	5	X
ap-4182	172	2	.	.	X
ap-4182	172	3	conclusion	conclusion	NOUN
ap-4182	172	4	we	we	PRON
ap-4182	172	5	developed	develop	VERB
ap-4182	172	6	a	a	DET
ap-4182	172	7	numerical	numerical	ADJ
ap-4182	172	8	method	method	NOUN
ap-4182	172	9	to	to	PART
ap-4182	172	10	determine	determine	VERB
ap-4182	172	11	a	a	DET
ap-4182	172	12	gauge	gauge	ADV
ap-4182	172	13	-	-	PUNCT
ap-4182	172	14	smoothed	smooth	VERB
ap-4182	172	15	biorthogonal	biorthogonal	ADJ
ap-4182	172	16	basis	basis	NOUN
ap-4182	172	17	of	of	ADP
ap-4182	172	18	eigenstates	eigenstate	NOUN
ap-4182	172	19	of	of	ADP
ap-4182	172	20	a	a	DET
ap-4182	172	21	pt	pt	NOUN
ap-4182	172	22	-symmetric	-symmetric	ADJ
ap-4182	172	23	non	non	ADJ
ap-4182	172	24	-	-	ADJ
ap-4182	172	25	hermitian	hermitian	ADJ
ap-4182	172	26	hamiltonian	hamiltonian	NOUN
ap-4182	172	27	required	require	VERB
ap-4182	172	28	for	for	ADP
ap-4182	172	29	complex	complex	ADJ
ap-4182	172	30	zak	zak	PROPN
ap-4182	172	31	phases	phase	NOUN
ap-4182	172	32	.	.	PUNCT
ap-4182	173	1	it	it	PRON
ap-4182	173	2	is	be	AUX
ap-4182	173	3	also	also	ADV
ap-4182	173	4	applicable	applicable	ADJ
ap-4182	173	5	to	to	ADP
ap-4182	173	6	hermitian	hermitian	ADJ
ap-4182	173	7	systems	system	NOUN
ap-4182	173	8	.	.	PUNCT
ap-4182	174	1	in	in	ADP
ap-4182	174	2	the	the	DET
ap-4182	174	3	course	course	NOUN
ap-4182	174	4	of	of	ADP
ap-4182	174	5	this	this	PRON
ap-4182	174	6	we	we	PRON
ap-4182	174	7	removed	remove	VERB
ap-4182	174	8	-2	-2	NOUN
ap-4182	174	9	0	0	NUM
ap-4182	174	10	2	2	NUM
ap-4182	174	11	(	(	PUNCT
ap-4182	174	12	a	a	NOUN
ap-4182	174	13	)	)	PUNCT
ap-4182	174	14	-2	-2	NOUN
ap-4182	174	15	0	0	NUM
ap-4182	174	16	2	2	NUM
ap-4182	174	17	-1	-1	SYM
ap-4182	174	18	-0.5	-0.5	X
ap-4182	174	19	0	0	NUM
ap-4182	174	20	0.5	0.5	NUM
ap-4182	174	21	1	1	NUM
ap-4182	174	22	re	re	VERB
ap-4182	174	23	i	i	PRON
ap-4182	174	24	m	m	VERB
ap-4182	174	25	(	(	PUNCT
ap-4182	174	26	b	b	NOUN
ap-4182	174	27	)	)	PUNCT
ap-4182	174	28	γ	γ	PROPN
ap-4182	174	29	1/	1/	NUM
ap-4182	174	30	π	π	SYM
ap-4182	174	31	γ	γ	X
ap-4182	174	32	2/	2/	NUM
ap-4182	174	33	π	π	SYM
ap-4182	174	34	θ	θ	PROPN
ap-4182	174	35	/	/	SYM
ap-4182	174	36	π	π	PROPN
ap-4182	174	37	analytic	analytic	ADJ
ap-4182	174	38	figure	figure	NOUN
ap-4182	174	39	3	3	NUM
ap-4182	174	40	.	.	PUNCT
ap-4182	175	1	(	(	PUNCT
ap-4182	175	2	colour	colour	NOUN
ap-4182	175	3	online	online	NOUN
ap-4182	175	4	)	)	PUNCT
ap-4182	175	5	numerical	numerical	ADJ
ap-4182	175	6	results	result	NOUN
ap-4182	175	7	of	of	ADP
ap-4182	175	8	the	the	DET
ap-4182	175	9	real	real	ADJ
ap-4182	175	10	part	part	NOUN
ap-4182	175	11	(	(	PUNCT
ap-4182	175	12	filled	fill	VERB
ap-4182	175	13	red	red	ADJ
ap-4182	175	14	dots	dot	NOUN
ap-4182	175	15	)	)	PUNCT
ap-4182	175	16	and	and	CCONJ
ap-4182	175	17	the	the	DET
ap-4182	175	18	imaginary	imaginary	ADJ
ap-4182	175	19	part	part	NOUN
ap-4182	175	20	(	(	PUNCT
ap-4182	175	21	open	open	ADJ
ap-4182	175	22	blue	blue	ADJ
ap-4182	175	23	circles	circle	NOUN
ap-4182	175	24	)	)	PUNCT
ap-4182	175	25	of	of	ADP
ap-4182	175	26	the	the	DET
ap-4182	175	27	complex	complex	ADJ
ap-4182	175	28	zak	zak	PROPN
ap-4182	175	29	phases	phase	NOUN
ap-4182	175	30	γ1	γ1	PROPN
ap-4182	175	31	(	(	PUNCT
ap-4182	175	32	a	a	NOUN
ap-4182	175	33	)	)	PUNCT
ap-4182	175	34	and	and	CCONJ
ap-4182	175	35	γ2	γ2	PROPN
ap-4182	175	36	(	(	PUNCT
ap-4182	175	37	b	b	NOUN
ap-4182	175	38	)	)	PUNCT
ap-4182	175	39	following	follow	VERB
ap-4182	175	40	from	from	ADP
ap-4182	175	41	the	the	DET
ap-4182	175	42	hamiltonian	hamiltonian	NOUN
ap-4182	175	43	given	give	VERB
ap-4182	175	44	in	in	ADP
ap-4182	175	45	(	(	PUNCT
ap-4182	175	46	17	17	NUM
ap-4182	175	47	)	)	PUNCT
ap-4182	175	48	in	in	ADP
ap-4182	175	49	dependence	dependence	NOUN
ap-4182	175	50	of	of	ADP
ap-4182	175	51	the	the	DET
ap-4182	175	52	control	control	NOUN
ap-4182	175	53	parameter	parameter	NOUN
ap-4182	175	54	θ	θ	PROPN
ap-4182	175	55	with	with	ADP
ap-4182	175	56	t	t	PROPN
ap-4182	175	57	=	=	SYM
ap-4182	175	58	1	1	NUM
ap-4182	175	59	,	,	PUNCT
ap-4182	175	60	∆	∆	PROPN
ap-4182	175	61	=	=	SYM
ap-4182	175	62	1/2	1/2	NUM
ap-4182	175	63	and	and	CCONJ
ap-4182	175	64	γ	γ	X
ap-4182	175	65	=	=	SYM
ap-4182	175	66	1	1	NUM
ap-4182	175	67	(	(	PUNCT
ap-4182	175	68	all	all	DET
ap-4182	175	69	values	value	NOUN
ap-4182	175	70	in	in	ADP
ap-4182	175	71	a.u	a.u	PROPN
ap-4182	175	72	.	.	PUNCT
ap-4182	175	73	)	)	PUNCT
ap-4182	175	74	compared	compare	VERB
ap-4182	175	75	to	to	ADP
ap-4182	175	76	the	the	DET
ap-4182	175	77	analytical	analytical	ADJ
ap-4182	175	78	result	result	NOUN
ap-4182	175	79	(	(	PUNCT
ap-4182	175	80	real	real	ADJ
ap-4182	175	81	and	and	CCONJ
ap-4182	175	82	imaginary	imaginary	ADJ
ap-4182	175	83	part	part	NOUN
ap-4182	175	84	are	be	AUX
ap-4182	175	85	represented	represent	VERB
ap-4182	175	86	by	by	ADP
ap-4182	175	87	a	a	DET
ap-4182	175	88	solid	solid	ADJ
ap-4182	175	89	black	black	ADJ
ap-4182	175	90	line	line	NOUN
ap-4182	175	91	coinciding	coincide	VERB
ap-4182	175	92	with	with	ADP
ap-4182	175	93	the	the	DET
ap-4182	175	94	numerical	numerical	ADJ
ap-4182	175	95	results	result	NOUN
ap-4182	175	96	)	)	PUNCT
ap-4182	175	97	following	follow	VERB
ap-4182	175	98	from	from	ADP
ap-4182	175	99	(	(	PUNCT
ap-4182	175	100	26	26	NUM
ap-4182	175	101	)	)	PUNCT
ap-4182	175	102	.	.	PUNCT
ap-4182	176	1	the	the	DET
ap-4182	176	2	grey	grey	PROPN
ap-4182	176	3	shaded	shade	VERB
ap-4182	176	4	area	area	NOUN
ap-4182	176	5	marks	mark	VERB
ap-4182	176	6	the	the	DET
ap-4182	176	7	pt	pt	NOUN
ap-4182	176	8	-broken	-broken	ADJ
ap-4182	176	9	phase	phase	NOUN
ap-4182	176	10	of	of	ADP
ap-4182	176	11	the	the	DET
ap-4182	176	12	bloch	bloch	PROPN
ap-4182	176	13	hamiltonian	hamiltonian	PROPN
ap-4182	176	14	.	.	PUNCT
ap-4182	177	1	the	the	DET
ap-4182	177	2	arbitrary	arbitrary	ADJ
ap-4182	177	3	and	and	CCONJ
ap-4182	177	4	unconnected	unconnected	ADJ
ap-4182	177	5	global	global	ADJ
ap-4182	177	6	phases	phase	NOUN
ap-4182	177	7	of	of	ADP
ap-4182	177	8	the	the	DET
ap-4182	177	9	biorthogonal	biorthogonal	ADJ
ap-4182	177	10	eigenstates	eigenstate	NOUN
ap-4182	177	11	of	of	ADP
ap-4182	177	12	the	the	DET
ap-4182	177	13	pt	pt	NOUN
ap-4182	177	14	-symmetric	-symmetric	ADJ
ap-4182	177	15	hamiltonian	hamiltonian	NOUN
ap-4182	177	16	at	at	ADP
ap-4182	177	17	each	each	DET
ap-4182	177	18	point	point	NOUN
ap-4182	177	19	in	in	ADP
ap-4182	177	20	parameter	parameter	NOUN
ap-4182	177	21	space	space	NOUN
ap-4182	177	22	and	and	CCONJ
ap-4182	177	23	made	make	VERB
ap-4182	177	24	the	the	DET
ap-4182	177	25	basis	basis	NOUN
ap-4182	177	26	single	single	ADV
ap-4182	177	27	-	-	PUNCT
ap-4182	177	28	valued	value	VERB
ap-4182	177	29	.	.	PUNCT
ap-4182	178	1	this	this	PRON
ap-4182	178	2	allows	allow	VERB
ap-4182	178	3	for	for	ADP
ap-4182	178	4	the	the	DET
ap-4182	178	5	calculation	calculation	NOUN
ap-4182	178	6	of	of	ADP
ap-4182	178	7	the	the	DET
ap-4182	178	8	complex	complex	ADJ
ap-4182	178	9	berry	berry	NOUN
ap-4182	178	10	phase	phase	NOUN
ap-4182	178	11	by	by	ADP
ap-4182	178	12	explicitly	explicitly	ADV
ap-4182	178	13	evaluating	evaluate	VERB
ap-4182	178	14	(	(	PUNCT
ap-4182	178	15	2	2	NUM
ap-4182	178	16	)	)	PUNCT
ap-4182	178	17	even	even	ADV
ap-4182	178	18	in	in	ADP
ap-4182	178	19	complicated	complicated	ADJ
ap-4182	178	20	lattice	lattice	NOUN
ap-4182	178	21	systems	system	NOUN
ap-4182	178	22	for	for	ADP
ap-4182	178	23	which	which	PRON
ap-4182	178	24	no	no	DET
ap-4182	178	25	analytical	analytical	ADJ
ap-4182	178	26	access	access	NOUN
ap-4182	178	27	to	to	ADP
ap-4182	178	28	the	the	DET
ap-4182	178	29	eigenstates	eigenstate	NOUN
ap-4182	178	30	is	be	AUX
ap-4182	178	31	approachable	approachable	ADJ
ap-4182	178	32	.	.	PUNCT
ap-4182	179	1	we	we	PRON
ap-4182	179	2	demonstrated	demonstrate	VERB
ap-4182	179	3	the	the	DET
ap-4182	179	4	action	action	NOUN
ap-4182	179	5	of	of	ADP
ap-4182	179	6	the	the	DET
ap-4182	179	7	gauge	gauge	NOUN
ap-4182	179	8	smoothing	smoothing	NOUN
ap-4182	179	9	method	method	NOUN
ap-4182	179	10	by	by	ADP
ap-4182	179	11	applying	apply	VERB
ap-4182	179	12	the	the	DET
ap-4182	179	13	developed	develop	VERB
ap-4182	179	14	algorithm	algorithm	NOUN
ap-4182	179	15	to	to	ADP
ap-4182	179	16	a	a	DET
ap-4182	179	17	pt	pt	INTJ
ap-4182	179	18	symmetric	symmetric	ADJ
ap-4182	179	19	extension	extension	NOUN
ap-4182	179	20	of	of	ADP
ap-4182	179	21	the	the	DET
ap-4182	179	22	ssh	ssh	NOUN
ap-4182	179	23	model	model	NOUN
ap-4182	179	24	.	.	PUNCT
ap-4182	180	1	an	an	DET
ap-4182	180	2	excellent	excellent	ADJ
ap-4182	180	3	agreement	agreement	NOUN
ap-4182	180	4	of	of	ADP
ap-4182	180	5	the	the	DET
ap-4182	180	6	numerical	numerical	ADJ
ap-4182	180	7	and	and	CCONJ
ap-4182	180	8	analytical	analytical	ADJ
ap-4182	180	9	results	result	NOUN
ap-4182	180	10	was	be	AUX
ap-4182	180	11	found	find	VERB
ap-4182	180	12	.	.	PUNCT
ap-4182	181	1	in	in	ADP
ap-4182	181	2	future	future	ADJ
ap-4182	181	3	work	work	NOUN
ap-4182	181	4	this	this	PRON
ap-4182	181	5	provides	provide	VERB
ap-4182	181	6	the	the	DET
ap-4182	181	7	basis	basis	NOUN
ap-4182	181	8	for	for	ADP
ap-4182	181	9	the	the	DET
ap-4182	181	10	identification	identification	NOUN
ap-4182	181	11	of	of	ADP
ap-4182	181	12	the	the	DET
ap-4182	181	13	zak	zak	PROPN
ap-4182	181	14	phase	phase	NOUN
ap-4182	181	15	as	as	ADP
ap-4182	181	16	topological	topological	ADJ
ap-4182	181	17	invariant	invariant	NOUN
ap-4182	181	18	in	in	ADP
ap-4182	181	19	many	many	ADJ
ap-4182	181	20	-	-	PUNCT
ap-4182	181	21	body	body	NOUN
ap-4182	181	22	systems	system	NOUN
ap-4182	181	23	with	with	ADP
ap-4182	181	24	arbitrary	arbitrary	ADJ
ap-4182	181	25	pt	pt	ADJ
ap-4182	181	26	-symmetric	-symmetric	ADJ
ap-4182	181	27	complex	complex	ADJ
ap-4182	181	28	potentials	potential	NOUN
ap-4182	181	29	.	.	PUNCT
ap-4182	182	1	references	reference	NOUN
ap-4182	182	2	[	[	X
ap-4182	182	3	1	1	X
ap-4182	182	4	]	]	PUNCT
ap-4182	182	5	v.	v.	CCONJ
ap-4182	182	6	mourik	mourik	PROPN
ap-4182	182	7	,	,	PUNCT
ap-4182	182	8	k.	k.	PROPN
ap-4182	182	9	zuo	zuo	PROPN
ap-4182	182	10	,	,	PUNCT
ap-4182	182	11	s.	s.	PROPN
ap-4182	182	12	m.	m.	PROPN
ap-4182	182	13	frolov	frolov	PROPN
ap-4182	182	14	,	,	PUNCT
ap-4182	182	15	et	et	PROPN
ap-4182	182	16	al	al	PROPN
ap-4182	182	17	.	.	PROPN
ap-4182	182	18	signatures	signature	NOUN
ap-4182	182	19	of	of	ADP
ap-4182	182	20	majorana	majorana	ADJ
ap-4182	182	21	fermions	fermion	NOUN
ap-4182	182	22	in	in	ADP
ap-4182	182	23	hybrid	hybrid	ADJ
ap-4182	182	24	superconductorsemiconductor	superconductorsemiconductor	NOUN
ap-4182	182	25	nanowire	nanowire	NOUN
ap-4182	182	26	devices	device	NOUN
ap-4182	182	27	.	.	PUNCT
ap-4182	183	1	science	science	NOUN
ap-4182	183	2	336:1003–1007	336:1003–1007	NUM
ap-4182	183	3	,	,	PUNCT
ap-4182	183	4	2012	2012	NUM
ap-4182	183	5	.	.	PUNCT
ap-4182	184	1	doi:10.1126	doi:10.1126	PROPN
ap-4182	184	2	/	/	SYM
ap-4182	184	3	science.1222360	science.1222360	PROPN
ap-4182	184	4	.	.	PUNCT
ap-4182	185	1	[	[	X
ap-4182	185	2	2	2	X
ap-4182	185	3	]	]	PUNCT
ap-4182	185	4	t.	t.	PROPN
ap-4182	185	5	d.	d.	PROPN
ap-4182	185	6	stanescu	stanescu	PROPN
ap-4182	185	7	,	,	PUNCT
ap-4182	185	8	s.	s.	PROPN
ap-4182	185	9	tewari	tewari	PROPN
ap-4182	185	10	.	.	PUNCT
ap-4182	186	1	majorana	majorana	PROPN
ap-4182	186	2	fermions	fermion	NOUN
ap-4182	186	3	in	in	ADP
ap-4182	186	4	semiconductor	semiconductor	NOUN
ap-4182	186	5	nanowires	nanowire	NOUN
ap-4182	186	6	:	:	PUNCT
ap-4182	186	7	fundamentals	fundamental	NOUN
ap-4182	186	8	,	,	PUNCT
ap-4182	186	9	modeling	modeling	NOUN
ap-4182	186	10	,	,	PUNCT
ap-4182	186	11	and	and	CCONJ
ap-4182	186	12	experiment	experiment	NOUN
ap-4182	186	13	.	.	PUNCT
ap-4182	187	1	j	j	PROPN
ap-4182	187	2	phys	phys	PROPN
ap-4182	187	3	:	:	PUNCT
ap-4182	187	4	condens	conden	NOUN
ap-4182	187	5	matter	matter	VERB
ap-4182	187	6	25(23):233201	25(23):233201	NUM
ap-4182	187	7	,	,	PUNCT
ap-4182	187	8	2013	2013	NUM
ap-4182	187	9	.	.	PUNCT
ap-4182	188	1	doi:10.1088/0953	doi:10.1088/0953	NOUN
ap-4182	188	2	-	-	PUNCT
ap-4182	188	3	8984/25/23/233201	8984/25/23/233201	NOUN
ap-4182	188	4	.	.	PUNCT
ap-4182	189	1	[	[	X
ap-4182	189	2	3	3	X
ap-4182	189	3	]	]	PUNCT
ap-4182	189	4	s.	s.	PROPN
ap-4182	189	5	r.	r.	PROPN
ap-4182	189	6	elliott	elliott	PROPN
ap-4182	189	7	,	,	PUNCT
ap-4182	189	8	m.	m.	NOUN
ap-4182	189	9	franz	franz	PROPN
ap-4182	189	10	.	.	PUNCT
ap-4182	190	1	colloquium	colloquium	NOUN
ap-4182	190	2	:	:	PUNCT
ap-4182	190	3	majorana	majorana	PROPN
ap-4182	190	4	fermions	fermion	NOUN
ap-4182	190	5	in	in	ADP
ap-4182	190	6	nuclear	nuclear	NOUN
ap-4182	190	7	,	,	PUNCT
ap-4182	190	8	particle	particle	NOUN
ap-4182	190	9	,	,	PUNCT
ap-4182	190	10	and	and	CCONJ
ap-4182	190	11	solid	solid	ADJ
ap-4182	190	12	-	-	PUNCT
ap-4182	190	13	state	state	NOUN
ap-4182	190	14	physics	physics	NOUN
ap-4182	190	15	.	.	PUNCT
ap-4182	191	1	rev	rev	PROPN
ap-4182	191	2	mod	mod	PROPN
ap-4182	191	3	phys	phys	PROPN
ap-4182	191	4	87:137–163	87:137–163	NUM
ap-4182	191	5	,	,	PUNCT
ap-4182	191	6	2015	2015	NUM
ap-4182	191	7	.	.	PUNCT
ap-4182	192	1	doi:10.1103	doi:10.1103	SYM
ap-4182	192	2	/	/	SYM
ap-4182	192	3	revmodphys.87.137	revmodphys.87.137	NOUN
ap-4182	192	4	.	.	PUNCT
ap-4182	193	1	[	[	X
ap-4182	193	2	4	4	NUM
ap-4182	193	3	]	]	PUNCT
ap-4182	193	4	a.	a.	NOUN
ap-4182	193	5	stern	stern	NOUN
ap-4182	193	6	,	,	PUNCT
ap-4182	193	7	n.	n.	PROPN
ap-4182	193	8	h.	h.	PROPN
ap-4182	193	9	lindner	lindner	PROPN
ap-4182	193	10	.	.	PUNCT
ap-4182	194	1	topological	topological	ADJ
ap-4182	194	2	quantum	quantum	ADJ
ap-4182	194	3	computation	computation	NOUN
ap-4182	194	4	—	—	PUNCT
ap-4182	194	5	from	from	ADP
ap-4182	194	6	basic	basic	ADJ
ap-4182	194	7	concepts	concept	NOUN
ap-4182	194	8	to	to	ADP
ap-4182	194	9	first	first	ADJ
ap-4182	194	10	experiments	experiment	NOUN
ap-4182	194	11	.	.	PUNCT
ap-4182	195	1	science	science	NOUN
ap-4182	195	2	339(6124):1179–1184	339(6124):1179–1184	NUM
ap-4182	195	3	,	,	PUNCT
ap-4182	195	4	2013	2013	NUM
ap-4182	195	5	.	.	PUNCT
ap-4182	196	1	doi:10.1126	doi:10.1126	PROPN
ap-4182	196	2	/	/	SYM
ap-4182	197	1	science.1231473	science.1231473	PROPN
ap-4182	197	2	.	.	NOUN
ap-4182	197	3	474	474	NUM
ap-4182	197	4	http://dx.doi.org/10.1126/science.1222360	http://dx.doi.org/10.1126/science.1222360	CCONJ
ap-4182	197	5	http://dx.doi.org/10.1088/0953-8984/25/23/233201	http://dx.doi.org/10.1088/0953-8984/25/23/233201	X
ap-4182	197	6	http://dx.doi.org/10.1103/revmodphys.87.137	http://dx.doi.org/10.1103/revmodphys.87.137	NOUN
ap-4182	197	7	http://dx.doi.org/10.1126/science.1231473	http://dx.doi.org/10.1126/science.1231473	X
ap-4182	197	8	vol	vol	NOUN
ap-4182	197	9	.	.	PROPN
ap-4182	197	10	57	57	NUM
ap-4182	197	11	no	no	NOUN
ap-4182	197	12	.	.	PUNCT
ap-4182	198	1	6/2017	6/2017	NUM
ap-4182	198	2	numerical	numerical	ADJ
ap-4182	198	3	calculation	calculation	NOUN
ap-4182	198	4	of	of	ADP
ap-4182	198	5	the	the	DET
ap-4182	198	6	complex	complex	ADJ
ap-4182	198	7	berry	berry	NOUN
ap-4182	198	8	phase	phase	NOUN
ap-4182	198	9	[	[	X
ap-4182	198	10	5	5	NUM
ap-4182	198	11	]	]	PUNCT
ap-4182	198	12	a.	a.	NOUN
ap-4182	198	13	carmele	carmele	PROPN
ap-4182	198	14	,	,	PUNCT
ap-4182	198	15	m.	m.	NOUN
ap-4182	198	16	heyl	heyl	PROPN
ap-4182	198	17	,	,	PUNCT
ap-4182	198	18	c.	c.	PROPN
ap-4182	198	19	kraus	kraus	PROPN
ap-4182	198	20	,	,	PUNCT
ap-4182	198	21	m.	m.	NOUN
ap-4182	198	22	dalmonte	dalmonte	PROPN
ap-4182	198	23	.	.	PUNCT
ap-4182	199	1	stretched	stretch	VERB
ap-4182	199	2	exponential	exponential	ADJ
ap-4182	199	3	decay	decay	NOUN
ap-4182	199	4	of	of	ADP
ap-4182	199	5	majorana	majorana	PROPN
ap-4182	199	6	edge	edge	NOUN
ap-4182	199	7	modes	mode	NOUN
ap-4182	199	8	in	in	ADP
ap-4182	199	9	many	many	ADJ
ap-4182	199	10	-	-	PUNCT
ap-4182	199	11	body	body	NOUN
ap-4182	199	12	localized	localize	VERB
ap-4182	199	13	kitaev	kitaev	NOUN
ap-4182	199	14	chains	chain	NOUN
ap-4182	199	15	under	under	ADP
ap-4182	199	16	dissipation	dissipation	NOUN
ap-4182	199	17	.	.	PUNCT
ap-4182	200	1	phys	phy	NOUN
ap-4182	200	2	rev	rev	VERB
ap-4182	200	3	b	b	PROPN
ap-4182	200	4	92	92	NUM
ap-4182	200	5	,	,	PUNCT
ap-4182	200	6	2015	2015	NUM
ap-4182	200	7	.	.	PUNCT
ap-4182	201	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	201	2	/	/	SYM
ap-4182	201	3	physrevb.92.195107	physrevb.92.195107	NOUN
ap-4182	201	4	.	.	PUNCT
ap-4182	202	1	[	[	X
ap-4182	202	2	6	6	NUM
ap-4182	202	3	]	]	PUNCT
ap-4182	202	4	c.-e	c.-e	NOUN
ap-4182	202	5	.	.	PUNCT
ap-4182	203	1	bardyn	bardyn	NOUN
ap-4182	203	2	,	,	PUNCT
ap-4182	203	3	m.	m.	NOUN
ap-4182	203	4	a.	a.	NOUN
ap-4182	203	5	baranov	baranov	PROPN
ap-4182	203	6	,	,	PUNCT
ap-4182	203	7	c.	c.	PROPN
ap-4182	203	8	v.	v.	PROPN
ap-4182	203	9	kraus	kraus	PROPN
ap-4182	203	10	,	,	PUNCT
ap-4182	203	11	et	et	PROPN
ap-4182	203	12	al	al	PROPN
ap-4182	203	13	.	.	PUNCT
ap-4182	203	14	topology	topology	NOUN
ap-4182	203	15	by	by	ADP
ap-4182	203	16	dissipation	dissipation	NOUN
ap-4182	203	17	.	.	PUNCT
ap-4182	204	1	new	new	ADJ
ap-4182	204	2	j	j	PROPN
ap-4182	204	3	phys	phys	PROPN
ap-4182	204	4	15(8):085001	15(8):085001	PROPN
ap-4182	204	5	,	,	PUNCT
ap-4182	204	6	2013	2013	NUM
ap-4182	204	7	.	.	PUNCT
ap-4182	205	1	doi:10.1088/1367	doi:10.1088/1367	NOUN
ap-4182	205	2	-	-	PUNCT
ap-4182	205	3	2630/15/8/085001	2630/15/8/085001	NUM
ap-4182	205	4	.	.	PUNCT
ap-4182	206	1	[	[	X
ap-4182	206	2	7	7	X
ap-4182	206	3	]	]	X
ap-4182	206	4	p.	p.	PROPN
ap-4182	206	5	san	san	PROPN
ap-4182	206	6	-	-	PUNCT
ap-4182	206	7	jose	jose	PROPN
ap-4182	206	8	,	,	PUNCT
ap-4182	206	9	j.	j.	PROPN
ap-4182	206	10	cayao	cayao	PROPN
ap-4182	206	11	,	,	PUNCT
ap-4182	206	12	e.	e.	PROPN
ap-4182	206	13	prada	prada	PROPN
ap-4182	206	14	,	,	PUNCT
ap-4182	206	15	r.	r.	PROPN
ap-4182	206	16	aguado	aguado	NOUN
ap-4182	206	17	.	.	PUNCT
ap-4182	207	1	majorana	majorana	PROPN
ap-4182	207	2	bound	bind	VERB
ap-4182	207	3	states	state	NOUN
ap-4182	207	4	from	from	ADP
ap-4182	207	5	exceptional	exceptional	ADJ
ap-4182	207	6	points	point	NOUN
ap-4182	207	7	in	in	ADP
ap-4182	207	8	non	non	ADJ
ap-4182	207	9	-	-	ADJ
ap-4182	207	10	topological	topological	ADJ
ap-4182	207	11	superconductors	superconductor	NOUN
ap-4182	207	12	.	.	PUNCT
ap-4182	208	1	sci	sci	PROPN
ap-4182	208	2	rep	rep	PROPN
ap-4182	208	3	6:21427	6:21427	NUM
ap-4182	208	4	,	,	PUNCT
ap-4182	208	5	2016	2016	NUM
ap-4182	208	6	.	.	PUNCT
ap-4182	209	1	doi:10.1038	doi:10.1038	NOUN
ap-4182	209	2	/	/	SYM
ap-4182	209	3	srep21427	srep21427	PROPN
ap-4182	209	4	.	.	PUNCT
ap-4182	210	1	[	[	X
ap-4182	210	2	8	8	NUM
ap-4182	210	3	]	]	X
ap-4182	210	4	c.	c.	PROPN
ap-4182	210	5	m.	m.	PROPN
ap-4182	210	6	bender	bender	PROPN
ap-4182	210	7	,	,	PUNCT
ap-4182	210	8	s.	s.	PROPN
ap-4182	210	9	boettcher	boettcher	PROPN
ap-4182	210	10	.	.	PUNCT
ap-4182	211	1	real	real	ADJ
ap-4182	211	2	spectra	spectra	NOUN
ap-4182	211	3	in	in	ADP
ap-4182	211	4	non	non	ADJ
ap-4182	211	5	-	-	ADJ
ap-4182	211	6	hermitian	hermitian	ADJ
ap-4182	211	7	hamiltonians	hamiltonian	NOUN
ap-4182	211	8	having	have	VERB
ap-4182	211	9	pt	pt	PRON
ap-4182	211	10	symmetry	symmetry	NOUN
ap-4182	211	11	.	.	PUNCT
ap-4182	212	1	phys	phy	NOUN
ap-4182	212	2	rev	rev	VERB
ap-4182	212	3	lett	lett	PROPN
ap-4182	212	4	80:5243–5246	80:5243–5246	PROPN
ap-4182	212	5	,	,	PUNCT
ap-4182	212	6	1998	1998	NUM
ap-4182	212	7	.	.	PUNCT
ap-4182	213	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	213	2	/	/	SYM
ap-4182	213	3	physrevlett.80.5243	physrevlett.80.5243	NOUN
ap-4182	213	4	.	.	PUNCT
ap-4182	214	1	[	[	X
ap-4182	214	2	9	9	NUM
ap-4182	214	3	]	]	PUNCT
ap-4182	214	4	m.	m.	NOUN
ap-4182	214	5	znojil	znojil	PROPN
ap-4182	214	6	.	.	PUNCT
ap-4182	215	1	pt	pt	PROPN
ap-4182	215	2	-symmetric	-symmetric	ADJ
ap-4182	215	3	square	square	PROPN
ap-4182	215	4	well	well	ADV
ap-4182	215	5	.	.	PUNCT
ap-4182	216	1	phys	phy	NOUN
ap-4182	216	2	lett	lett	VERB
ap-4182	216	3	a	a	DET
ap-4182	216	4	285(1–2):7	285(1–2):7	NUM
ap-4182	216	5	,	,	PUNCT
ap-4182	216	6	2001	2001	NUM
ap-4182	216	7	.	.	PUNCT
ap-4182	217	1	doi:10.1016	doi:10.1016	PROPN
ap-4182	217	2	/	/	SYM
ap-4182	217	3	s0375	s0375	PROPN
ap-4182	217	4	-	-	PUNCT
ap-4182	217	5	9601(01)00301	9601(01)00301	NUM
ap-4182	217	6	-	-	SYM
ap-4182	217	7	2	2	NUM
ap-4182	217	8	.	.	PUNCT
ap-4182	218	1	[	[	X
ap-4182	218	2	10	10	NUM
ap-4182	218	3	]	]	X
ap-4182	218	4	c.	c.	PROPN
ap-4182	218	5	m.	m.	PROPN
ap-4182	218	6	bender	bender	PROPN
ap-4182	218	7	,	,	PUNCT
ap-4182	218	8	d.	d.	PROPN
ap-4182	218	9	c.	c.	PROPN
ap-4182	218	10	brody	brody	PROPN
ap-4182	218	11	,	,	PUNCT
ap-4182	218	12	h.	h.	PROPN
ap-4182	218	13	f.	f.	PROPN
ap-4182	218	14	jones	jones	PROPN
ap-4182	218	15	.	.	PUNCT
ap-4182	219	1	complex	complex	ADJ
ap-4182	219	2	extension	extension	NOUN
ap-4182	219	3	of	of	ADP
ap-4182	219	4	quantum	quantum	ADJ
ap-4182	219	5	mechanics	mechanic	NOUN
ap-4182	219	6	.	.	PUNCT
ap-4182	220	1	phys	phy	NOUN
ap-4182	220	2	rev	rev	VERB
ap-4182	220	3	lett	lett	PROPN
ap-4182	220	4	89:270401	89:270401	PROPN
ap-4182	220	5	,	,	PUNCT
ap-4182	220	6	2002	2002	NUM
ap-4182	220	7	.	.	PUNCT
ap-4182	221	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	221	2	/	/	SYM
ap-4182	221	3	physrevlett.89.270401	physrevlett.89.270401	NOUN
ap-4182	221	4	.	.	PUNCT
ap-4182	222	1	[	[	X
ap-4182	222	2	11	11	NUM
ap-4182	222	3	]	]	PUNCT
ap-4182	222	4	m.	m.	NOUN
ap-4182	222	5	znojil	znojil	PROPN
ap-4182	222	6	.	.	PUNCT
ap-4182	223	1	decays	decay	NOUN
ap-4182	223	2	of	of	ADP
ap-4182	223	3	degeneracies	degeneracy	NOUN
ap-4182	223	4	in	in	ADP
ap-4182	223	5	pt	pt	NOUN
ap-4182	223	6	-symmetric	-symmetric	ADJ
ap-4182	223	7	ring	ring	NOUN
ap-4182	223	8	-	-	PUNCT
ap-4182	223	9	shaped	shape	VERB
ap-4182	223	10	lattices	lattice	NOUN
ap-4182	223	11	.	.	PUNCT
ap-4182	224	1	phys	phy	NOUN
ap-4182	224	2	lett	lett	VERB
ap-4182	224	3	a	a	DET
ap-4182	224	4	375(39):3435	375(39):3435	PROPN
ap-4182	224	5	,	,	PUNCT
ap-4182	224	6	2011	2011	NUM
ap-4182	224	7	.	.	PUNCT
ap-4182	225	1	doi:10.1016	doi:10.1016	PROPN
ap-4182	225	2	/	/	SYM
ap-4182	225	3	j.physleta.2011.08.005	j.physleta.2011.08.005	PROPN
ap-4182	225	4	.	.	PUNCT
ap-4182	226	1	[	[	X
ap-4182	226	2	12	12	NUM
ap-4182	226	3	]	]	PUNCT
ap-4182	226	4	h.	h.	PROPN
ap-4182	226	5	f.	f.	PROPN
ap-4182	226	6	jones	jones	PROPN
ap-4182	226	7	,	,	PUNCT
ap-4182	226	8	e.	e.	PROPN
ap-4182	226	9	s.	s.	PROPN
ap-4182	226	10	moreira	moreira	PROPN
ap-4182	226	11	,	,	PUNCT
ap-4182	226	12	jr	jr	PROPN
ap-4182	226	13	.	.	PROPN
ap-4182	226	14	quantum	quantum	ADJ
ap-4182	226	15	and	and	CCONJ
ap-4182	226	16	classical	classical	ADJ
ap-4182	226	17	statistical	statistical	ADJ
ap-4182	226	18	mechanics	mechanic	NOUN
ap-4182	226	19	of	of	ADP
ap-4182	226	20	a	a	DET
ap-4182	226	21	class	class	NOUN
ap-4182	226	22	of	of	ADP
ap-4182	226	23	non	non	ADJ
ap-4182	226	24	-	-	ADJ
ap-4182	226	25	hermitian	hermitian	ADJ
ap-4182	226	26	hamiltonians	hamiltonian	NOUN
ap-4182	226	27	.	.	PUNCT
ap-4182	227	1	j	j	PROPN
ap-4182	227	2	phys	phy	NOUN
ap-4182	227	3	a	a	DET
ap-4182	227	4	43(5):055307	43(5):055307	NUM
ap-4182	227	5	,	,	PUNCT
ap-4182	227	6	2010	2010	NUM
ap-4182	227	7	.	.	PUNCT
ap-4182	228	1	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-4182	228	2	-	-	PUNCT
ap-4182	228	3	8113/43/5/055307	8113/43/5/055307	NUM
ap-4182	228	4	.	.	PUNCT
ap-4182	229	1	[	[	X
ap-4182	229	2	13	13	NUM
ap-4182	229	3	]	]	PUNCT
ap-4182	229	4	k.	k.	PROPN
ap-4182	229	5	li	li	PROPN
ap-4182	229	6	,	,	PUNCT
ap-4182	229	7	p.	p.	PROPN
ap-4182	229	8	g.	g.	PROPN
ap-4182	229	9	kevrekidis	kevrekidis	PROPN
ap-4182	229	10	,	,	PUNCT
ap-4182	229	11	b.	b.	PROPN
ap-4182	229	12	a.	a.	PROPN
ap-4182	229	13	malomed	malomed	PROPN
ap-4182	229	14	,	,	PUNCT
ap-4182	229	15	u.	u.	PROPN
ap-4182	229	16	günther	günther	PROPN
ap-4182	229	17	.	.	PUNCT
ap-4182	230	1	nonlinear	nonlinear	ADJ
ap-4182	230	2	pt	pt	CCONJ
ap-4182	230	3	-symmetric	-symmetric	ADJ
ap-4182	230	4	plaquettes	plaquette	NOUN
ap-4182	230	5	.	.	PUNCT
ap-4182	231	1	j	j	PROPN
ap-4182	231	2	phys	phy	NOUN
ap-4182	231	3	a	a	DET
ap-4182	231	4	45(44):444021	45(44):444021	NUM
ap-4182	231	5	,	,	PUNCT
ap-4182	231	6	2012	2012	NUM
ap-4182	231	7	.	.	PUNCT
ap-4182	232	1	doi:10.1088/1751	doi:10.1088/1751	PROPN
ap-4182	232	2	-	-	PUNCT
ap-4182	232	3	8113/45/44/444021	8113/45/44/444021	NUM
ap-4182	232	4	.	.	PUNCT
ap-4182	233	1	[	[	X
ap-4182	233	2	14	14	NUM
ap-4182	233	3	]	]	X
ap-4182	233	4	h.	h.	PROPN
ap-4182	233	5	mehri	mehri	PROPN
ap-4182	233	6	-	-	PUNCT
ap-4182	233	7	dehnavi	dehnavi	ADV
ap-4182	233	8	,	,	PUNCT
ap-4182	233	9	a.	a.	NOUN
ap-4182	233	10	mostafazadeh	mostafazadeh	PROPN
ap-4182	233	11	,	,	PUNCT
ap-4182	233	12	a.	a.	PROPN
ap-4182	233	13	batal	batal	PROPN
ap-4182	233	14	.	.	PUNCT
ap-4182	234	1	application	application	NOUN
ap-4182	234	2	of	of	ADP
ap-4182	234	3	pseudo	pseudo	NOUN
ap-4182	234	4	-	-	ADJ
ap-4182	234	5	hermitian	hermitian	ADJ
ap-4182	234	6	quantum	quantum	ADJ
ap-4182	234	7	mechanics	mechanic	NOUN
ap-4182	234	8	to	to	ADP
ap-4182	234	9	a	a	DET
ap-4182	234	10	complex	complex	ADJ
ap-4182	234	11	scattering	scattering	ADJ
ap-4182	234	12	potential	potential	NOUN
ap-4182	234	13	with	with	ADP
ap-4182	234	14	point	point	NOUN
ap-4182	234	15	interactions	interaction	NOUN
ap-4182	234	16	.	.	PUNCT
ap-4182	235	1	j	j	PROPN
ap-4182	235	2	phys	phy	NOUN
ap-4182	235	3	a	a	DET
ap-4182	235	4	43:145301	43:145301	NUM
ap-4182	235	5	,	,	PUNCT
ap-4182	235	6	2010	2010	NUM
ap-4182	235	7	.	.	PUNCT
ap-4182	236	1	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-4182	236	2	-	-	PUNCT
ap-4182	236	3	8113/43/14/145301	8113/43/14/145301	NUM
ap-4182	236	4	.	.	PUNCT
ap-4182	237	1	[	[	X
ap-4182	237	2	15	15	NUM
ap-4182	237	3	]	]	X
ap-4182	237	4	v.	v.	CCONJ
ap-4182	237	5	jakubský	jakubský	PROPN
ap-4182	237	6	,	,	PUNCT
ap-4182	237	7	m.	m.	NOUN
ap-4182	237	8	znojil	znojil	PROPN
ap-4182	237	9	.	.	PUNCT
ap-4182	238	1	an	an	DET
ap-4182	238	2	explicitly	explicitly	ADV
ap-4182	238	3	solvable	solvable	ADJ
ap-4182	238	4	model	model	NOUN
ap-4182	238	5	of	of	ADP
ap-4182	238	6	the	the	DET
ap-4182	238	7	spontaneous	spontaneous	ADJ
ap-4182	238	8	pt	pt	PROPN
ap-4182	238	9	-symmetry	-symmetry	NOUN
ap-4182	238	10	breaking	breaking	NOUN
ap-4182	238	11	.	.	PUNCT
ap-4182	239	1	czech	czech	PROPN
ap-4182	239	2	j	j	PROPN
ap-4182	239	3	phys	phys	PROPN
ap-4182	239	4	55:1113	55:1113	NUM
ap-4182	239	5	,	,	PUNCT
ap-4182	239	6	2005	2005	NUM
ap-4182	239	7	.	.	PUNCT
ap-4182	240	1	doi:10.1007	doi:10.1007	VERB
ap-4182	240	2	/	/	SYM
ap-4182	240	3	s10582	s10582	VERB
ap-4182	240	4	-	-	PUNCT
ap-4182	240	5	005	005	NUM
ap-4182	240	6	-	-	PUNCT
ap-4182	240	7	0115	0115	NUM
ap-4182	240	8	-	-	PUNCT
ap-4182	240	9	x.	x.	NOUN
ap-4182	241	1	[	[	X
ap-4182	241	2	16	16	NUM
ap-4182	241	3	]	]	X
ap-4182	241	4	g.	g.	PROPN
ap-4182	241	5	lévai	lévai	PROPN
ap-4182	241	6	,	,	PUNCT
ap-4182	241	7	m.	m.	NOUN
ap-4182	241	8	znojil	znojil	PROPN
ap-4182	241	9	.	.	PUNCT
ap-4182	242	1	the	the	DET
ap-4182	242	2	interplay	interplay	NOUN
ap-4182	242	3	of	of	ADP
ap-4182	242	4	supersymmetry	supersymmetry	NOUN
ap-4182	242	5	and	and	CCONJ
ap-4182	242	6	pt	pt	NOUN
ap-4182	242	7	symmetry	symmetry	NOUN
ap-4182	242	8	in	in	ADP
ap-4182	242	9	quantum	quantum	ADJ
ap-4182	242	10	mechanics	mechanic	NOUN
ap-4182	242	11	:	:	PUNCT
ap-4182	242	12	a	a	DET
ap-4182	242	13	case	case	NOUN
ap-4182	242	14	study	study	NOUN
ap-4182	242	15	for	for	ADP
ap-4182	242	16	the	the	DET
ap-4182	242	17	scarf	scarf	PROPN
ap-4182	242	18	ii	ii	PROPN
ap-4182	242	19	potential	potential	NOUN
ap-4182	242	20	.	.	PUNCT
ap-4182	243	1	j	j	PROPN
ap-4182	243	2	phys	phy	NOUN
ap-4182	243	3	a	a	DET
ap-4182	243	4	35(41):8793	35(41):8793	NUM
ap-4182	243	5	,	,	PUNCT
ap-4182	243	6	2002	2002	NUM
ap-4182	243	7	.	.	PUNCT
ap-4182	244	1	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-4182	244	2	-	-	PUNCT
ap-4182	244	3	4470/35/41/311	4470/35/41/311	NUM
ap-4182	244	4	.	.	PUNCT
ap-4182	245	1	[	[	X
ap-4182	245	2	17	17	NUM
ap-4182	245	3	]	]	X
ap-4182	245	4	n.	n.	PROPN
ap-4182	245	5	abt	abt	PROPN
ap-4182	245	6	,	,	PUNCT
ap-4182	245	7	h.	h.	PROPN
ap-4182	245	8	cartarius	cartarius	PROPN
ap-4182	245	9	,	,	PUNCT
ap-4182	245	10	g.	g.	PROPN
ap-4182	245	11	wunner	wunner	PROPN
ap-4182	245	12	.	.	PUNCT
ap-4182	246	1	supersymmetric	supersymmetric	ADJ
ap-4182	246	2	model	model	NOUN
ap-4182	246	3	of	of	ADP
ap-4182	246	4	a	a	DET
ap-4182	246	5	bose	bose	NOUN
ap-4182	246	6	-	-	PUNCT
ap-4182	246	7	einstein	einstein	NOUN
ap-4182	246	8	condensate	condensate	NOUN
ap-4182	246	9	in	in	ADP
ap-4182	246	10	a	a	DET
ap-4182	246	11	pt	pt	NOUN
ap-4182	246	12	-symmetric	-symmetric	ADJ
ap-4182	246	13	double	double	ADJ
ap-4182	246	14	-	-	PUNCT
ap-4182	246	15	delta	delta	NOUN
ap-4182	246	16	trap	trap	NOUN
ap-4182	246	17	.	.	PUNCT
ap-4182	247	1	int	int	PROPN
ap-4182	248	1	j	j	PROPN
ap-4182	248	2	theor	theor	PROPN
ap-4182	248	3	phys	phys	PROPN
ap-4182	248	4	54(11):4054–4067	54(11):4054–4067	PROPN
ap-4182	248	5	,	,	PUNCT
ap-4182	248	6	2015	2015	NUM
ap-4182	248	7	.	.	PUNCT
ap-4182	249	1	doi:10.1007	doi:10.1007	VERB
ap-4182	249	2	/	/	SYM
ap-4182	249	3	s10773	s10773	NUM
ap-4182	249	4	-	-	PUNCT
ap-4182	249	5	014	014	NUM
ap-4182	249	6	-	-	PUNCT
ap-4182	249	7	2467	2467	NUM
ap-4182	249	8	-	-	SYM
ap-4182	249	9	0	0	NUM
ap-4182	249	10	.	.	PUNCT
ap-4182	250	1	[	[	X
ap-4182	250	2	18	18	NUM
ap-4182	250	3	]	]	PUNCT
ap-4182	250	4	a.	a.	NOUN
ap-4182	250	5	mostafazadeh	mostafazadeh	PROPN
ap-4182	250	6	.	.	PUNCT
ap-4182	251	1	delta	delta	ADJ
ap-4182	251	2	-	-	PUNCT
ap-4182	251	3	function	function	NOUN
ap-4182	251	4	potential	potential	NOUN
ap-4182	251	5	with	with	ADP
ap-4182	251	6	a	a	DET
ap-4182	251	7	complex	complex	ADJ
ap-4182	251	8	coupling	coupling	NOUN
ap-4182	251	9	.	.	PUNCT
ap-4182	252	1	j	j	PROPN
ap-4182	252	2	phys	phy	NOUN
ap-4182	252	3	a	a	DET
ap-4182	252	4	39:13495	39:13495	NUM
ap-4182	252	5	,	,	PUNCT
ap-4182	252	6	2006	2006	NUM
ap-4182	252	7	.	.	PUNCT
ap-4182	253	1	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-4182	253	2	-	-	PUNCT
ap-4182	253	3	4470/39/43/008	4470/39/43/008	NOUN
ap-4182	253	4	.	.	PUNCT
ap-4182	254	1	[	[	X
ap-4182	254	2	19	19	NUM
ap-4182	254	3	]	]	X
ap-4182	254	4	h.	h.	PROPN
ap-4182	254	5	f.	f.	PROPN
ap-4182	254	6	jones	jones	PROPN
ap-4182	254	7	.	.	PROPN
ap-4182	255	1	interface	interface	PROPN
ap-4182	255	2	between	between	ADP
ap-4182	255	3	hermitian	hermitian	PROPN
ap-4182	255	4	and	and	CCONJ
ap-4182	255	5	nonhermitian	nonhermitian	ADJ
ap-4182	255	6	hamiltonians	hamiltonian	NOUN
ap-4182	255	7	in	in	ADP
ap-4182	255	8	a	a	DET
ap-4182	255	9	model	model	NOUN
ap-4182	255	10	calculation	calculation	NOUN
ap-4182	255	11	.	.	PUNCT
ap-4182	256	1	phys	phy	NOUN
ap-4182	256	2	rev	rev	VERB
ap-4182	256	3	d	d	PROPN
ap-4182	256	4	78:065032	78:065032	NUM
ap-4182	256	5	,	,	PUNCT
ap-4182	256	6	2008	2008	NUM
ap-4182	256	7	.	.	PUNCT
ap-4182	257	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	257	2	/	/	SYM
ap-4182	257	3	physrevd.78.065032	physrevd.78.065032	NOUN
ap-4182	257	4	.	.	PUNCT
ap-4182	258	1	[	[	X
ap-4182	258	2	20	20	NUM
ap-4182	258	3	]	]	X
ap-4182	258	4	e.	e.	PROPN
ap-4182	258	5	m.	m.	PROPN
ap-4182	258	6	graefe	graefe	PROPN
ap-4182	258	7	,	,	PUNCT
ap-4182	258	8	h.	h.	PROPN
ap-4182	258	9	j.	j.	PROPN
ap-4182	258	10	korsch	korsch	PROPN
ap-4182	258	11	,	,	PUNCT
ap-4182	258	12	a.	a.	PROPN
ap-4182	258	13	e.	e.	PROPN
ap-4182	258	14	niederle	niederle	PROPN
ap-4182	258	15	.	.	PUNCT
ap-4182	259	1	mean	mean	ADJ
ap-4182	259	2	-	-	PUNCT
ap-4182	259	3	field	field	NOUN
ap-4182	259	4	dynamics	dynamic	NOUN
ap-4182	259	5	of	of	ADP
ap-4182	259	6	a	a	DET
ap-4182	259	7	non	non	ADJ
ap-4182	259	8	-	-	ADJ
ap-4182	259	9	hermitian	hermitian	ADJ
ap-4182	259	10	bose	bose	PROPN
ap-4182	259	11	-	-	PUNCT
ap-4182	259	12	hubbard	hubbard	NOUN
ap-4182	259	13	dimer	dimer	NOUN
ap-4182	259	14	.	.	PUNCT
ap-4182	260	1	phys	phy	NOUN
ap-4182	260	2	rev	rev	VERB
ap-4182	260	3	lett	lett	PROPN
ap-4182	260	4	101:150408	101:150408	NUM
ap-4182	260	5	,	,	PUNCT
ap-4182	260	6	2008	2008	NUM
ap-4182	260	7	.	.	PUNCT
ap-4182	261	1	doi:10.1103	doi:10.1103	PROPN
ap-4182	261	2	/	/	SYM
ap-4182	261	3	physrevlett.101.150408	physrevlett.101.150408	X
ap-4182	261	4	.	.	PUNCT
ap-4182	262	1	[	[	X
ap-4182	262	2	21	21	NUM
ap-4182	262	3	]	]	X
ap-4182	262	4	e.	e.	PROPN
ap-4182	262	5	m.	m.	PROPN
ap-4182	262	6	graefe	graefe	PROPN
ap-4182	262	7	,	,	PUNCT
ap-4182	262	8	u.	u.	PROPN
ap-4182	262	9	günther	günther	PROPN
ap-4182	262	10	,	,	PUNCT
ap-4182	262	11	h.	h.	PROPN
ap-4182	262	12	j.	j.	PROPN
ap-4182	262	13	korsch	korsch	PROPN
ap-4182	262	14	,	,	PUNCT
ap-4182	262	15	a.	a.	PROPN
ap-4182	262	16	e.	e.	PROPN
ap-4182	262	17	niederle	niederle	PROPN
ap-4182	262	18	.	.	PUNCT
ap-4182	263	1	a	a	DET
ap-4182	263	2	non	non	ADJ
ap-4182	263	3	-	-	ADJ
ap-4182	263	4	hermitian	hermitian	ADJ
ap-4182	263	5	pt	pt	PROPN
ap-4182	263	6	symmetric	symmetric	PROPN
ap-4182	263	7	bose	bose	PROPN
ap-4182	263	8	-	-	PUNCT
ap-4182	263	9	hubbard	hubbard	NOUN
ap-4182	263	10	model	model	NOUN
ap-4182	263	11	:	:	PUNCT
ap-4182	263	12	eigenvalue	eigenvalue	NOUN
ap-4182	263	13	rings	ring	NOUN
ap-4182	263	14	from	from	ADP
ap-4182	263	15	unfolding	unfold	VERB
ap-4182	263	16	higher	high	ADJ
ap-4182	263	17	-	-	PUNCT
ap-4182	263	18	order	order	NOUN
ap-4182	263	19	exceptional	exceptional	ADJ
ap-4182	263	20	points	point	NOUN
ap-4182	263	21	.	.	PUNCT
ap-4182	264	1	j	j	PROPN
ap-4182	264	2	phy	phy	PROPN
ap-4182	264	3	a	a	DET
ap-4182	264	4	41(25):255206	41(25):255206	NUM
ap-4182	264	5	,	,	PUNCT
ap-4182	264	6	2008	2008	NUM
ap-4182	264	7	.	.	PUNCT
ap-4182	265	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-4182	265	2	-	-	PUNCT
ap-4182	265	3	8113/41/25/255206	8113/41/25/255206	NUM
ap-4182	265	4	.	.	PUNCT
ap-4182	266	1	[	[	X
ap-4182	266	2	22	22	NUM
ap-4182	266	3	]	]	PUNCT
ap-4182	266	4	z.	z.	PROPN
ap-4182	266	5	h.	h.	PROPN
ap-4182	266	6	musslimani	musslimani	PROPN
ap-4182	266	7	,	,	PUNCT
ap-4182	266	8	k.	k.	PROPN
ap-4182	266	9	g.	g.	PROPN
ap-4182	266	10	makris	makris	PROPN
ap-4182	266	11	,	,	PUNCT
ap-4182	266	12	r.	r.	PROPN
ap-4182	266	13	el	el	PROPN
ap-4182	266	14	-	-	PUNCT
ap-4182	266	15	ganainy	ganainy	PROPN
ap-4182	266	16	,	,	PUNCT
ap-4182	266	17	d.	d.	PROPN
ap-4182	266	18	n.	n.	PROPN
ap-4182	266	19	christodoulides	christodoulide	NOUN
ap-4182	266	20	.	.	PUNCT
ap-4182	267	1	analytical	analytical	ADJ
ap-4182	267	2	solutions	solution	NOUN
ap-4182	267	3	to	to	ADP
ap-4182	267	4	a	a	DET
ap-4182	267	5	class	class	NOUN
ap-4182	267	6	of	of	ADP
ap-4182	267	7	nonlinear	nonlinear	ADJ
ap-4182	267	8	schrödinger	schrödinger	ADJ
ap-4182	267	9	equations	equation	NOUN
ap-4182	267	10	with	with	ADP
ap-4182	267	11	pt	pt	X
ap-4182	267	12	-like	-like	PROPN
ap-4182	267	13	potentials	potential	NOUN
ap-4182	267	14	.	.	PUNCT
ap-4182	268	1	j	j	PROPN
ap-4182	268	2	phys	phy	NOUN
ap-4182	268	3	a	a	DET
ap-4182	268	4	41:244019	41:244019	NUM
ap-4182	268	5	,	,	PUNCT
ap-4182	268	6	2008	2008	NUM
ap-4182	268	7	.	.	PUNCT
ap-4182	269	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-4182	269	2	-	-	PUNCT
ap-4182	269	3	8113/41/24/244019	8113/41/24/244019	NUM
ap-4182	269	4	.	.	PUNCT
ap-4182	270	1	[	[	X
ap-4182	270	2	23	23	NUM
ap-4182	270	3	]	]	X
ap-4182	270	4	w.	w.	PROPN
ap-4182	270	5	d.	d.	PROPN
ap-4182	270	6	heiss	heiss	PROPN
ap-4182	270	7	,	,	PUNCT
ap-4182	270	8	h.	h.	PROPN
ap-4182	270	9	cartarius	cartarius	PROPN
ap-4182	270	10	,	,	PUNCT
ap-4182	270	11	g.	g.	PROPN
ap-4182	270	12	wunner	wunner	PROPN
ap-4182	270	13	,	,	PUNCT
ap-4182	270	14	j.	j.	PROPN
ap-4182	270	15	main	main	PROPN
ap-4182	270	16	.	.	PUNCT
ap-4182	271	1	spectral	spectral	ADJ
ap-4182	271	2	singularities	singularity	NOUN
ap-4182	271	3	in	in	ADP
ap-4182	271	4	pt	pt	X
ap-4182	271	5	-symmetric	-symmetric	ADJ
ap-4182	271	6	bose	bose	NOUN
ap-4182	271	7	-	-	PUNCT
ap-4182	271	8	einstein	einstein	NOUN
ap-4182	271	9	condensates	condensate	NOUN
ap-4182	271	10	.	.	PUNCT
ap-4182	272	1	j	j	PROPN
ap-4182	272	2	phys	phy	NOUN
ap-4182	272	3	a	a	DET
ap-4182	272	4	46(27):275307	46(27):275307	NUM
ap-4182	272	5	,	,	PUNCT
ap-4182	272	6	2013	2013	NUM
ap-4182	272	7	.	.	PUNCT
ap-4182	273	1	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-4182	273	2	-	-	PUNCT
ap-4182	273	3	8113/46/27/275307	8113/46/27/275307	NUM
ap-4182	273	4	.	.	PUNCT
ap-4182	274	1	[	[	X
ap-4182	274	2	24	24	NUM
ap-4182	274	3	]	]	X
ap-4182	274	4	d.	d.	PROPN
ap-4182	274	5	dast	dast	PROPN
ap-4182	274	6	,	,	PUNCT
ap-4182	274	7	d.	d.	PROPN
ap-4182	274	8	haag	haag	PROPN
ap-4182	274	9	,	,	PUNCT
ap-4182	274	10	h.	h.	PROPN
ap-4182	274	11	cartarius	cartarius	PROPN
ap-4182	274	12	,	,	PUNCT
ap-4182	274	13	g.	g.	PROPN
ap-4182	274	14	wunner	wunner	NOUN
ap-4182	274	15	.	.	PUNCT
ap-4182	275	1	quantum	quantum	ADJ
ap-4182	275	2	master	master	NOUN
ap-4182	275	3	equation	equation	NOUN
ap-4182	275	4	with	with	ADP
ap-4182	275	5	balanced	balanced	ADJ
ap-4182	275	6	gain	gain	NOUN
ap-4182	275	7	and	and	CCONJ
ap-4182	275	8	loss	loss	NOUN
ap-4182	275	9	.	.	PUNCT
ap-4182	276	1	phys	phy	NOUN
ap-4182	276	2	rev	rev	VERB
ap-4182	276	3	a	a	DET
ap-4182	276	4	90:052120	90:052120	NUM
ap-4182	276	5	,	,	PUNCT
ap-4182	276	6	2014	2014	NUM
ap-4182	276	7	.	.	PUNCT
ap-4182	277	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	277	2	/	/	SYM
ap-4182	277	3	physreva.90.052120	physreva.90.052120	NOUN
ap-4182	277	4	.	.	PUNCT
ap-4182	278	1	[	[	X
ap-4182	278	2	25	25	NUM
ap-4182	278	3	]	]	X
ap-4182	278	4	r.	r.	PROPN
ap-4182	278	5	gutöhrlein	gutöhrlein	PROPN
ap-4182	278	6	,	,	PUNCT
ap-4182	278	7	j.	j.	PROPN
ap-4182	278	8	schnabel	schnabel	PROPN
ap-4182	278	9	,	,	PUNCT
ap-4182	278	10	i.	i.	PROPN
ap-4182	278	11	iskandarov	iskandarov	PROPN
ap-4182	278	12	,	,	PUNCT
ap-4182	278	13	et	et	PROPN
ap-4182	278	14	al	al	PROPN
ap-4182	278	15	.	.	PUNCT
ap-4182	278	16	realizing	realize	VERB
ap-4182	278	17	pt	pt	NOUN
ap-4182	278	18	-symmetric	-symmetric	ADJ
ap-4182	278	19	bec	bec	PROPN
ap-4182	278	20	subsystems	subsystem	NOUN
ap-4182	278	21	in	in	ADP
ap-4182	278	22	closed	closed	ADJ
ap-4182	278	23	hermitian	hermitian	ADJ
ap-4182	278	24	systems	system	NOUN
ap-4182	278	25	.	.	PUNCT
ap-4182	279	1	j	j	PROPN
ap-4182	279	2	phys	phy	NOUN
ap-4182	279	3	a	a	DET
ap-4182	279	4	48(33):335302	48(33):335302	NUM
ap-4182	279	5	,	,	PUNCT
ap-4182	279	6	2015	2015	NUM
ap-4182	279	7	.	.	PUNCT
ap-4182	280	1	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-4182	280	2	-	-	PUNCT
ap-4182	280	3	8113/48/33/335302	8113/48/33/335302	NUM
ap-4182	280	4	.	.	PUNCT
ap-4182	281	1	[	[	X
ap-4182	281	2	26	26	NUM
ap-4182	281	3	]	]	X
ap-4182	281	4	y.	y.	PROPN
ap-4182	281	5	c.	c.	PROPN
ap-4182	281	6	hu	hu	PROPN
ap-4182	281	7	,	,	PUNCT
ap-4182	281	8	t.	t.	PROPN
ap-4182	281	9	l.	l.	PROPN
ap-4182	281	10	hughes	hughes	PROPN
ap-4182	281	11	.	.	PUNCT
ap-4182	282	1	absence	absence	NOUN
ap-4182	282	2	of	of	ADP
ap-4182	282	3	topological	topological	ADJ
ap-4182	282	4	insulator	insulator	NOUN
ap-4182	282	5	phases	phase	NOUN
ap-4182	282	6	in	in	ADP
ap-4182	282	7	non	non	ADJ
ap-4182	282	8	-	-	ADJ
ap-4182	282	9	hermitian	hermitian	ADJ
ap-4182	282	10	pt	pt	NOUN
ap-4182	282	11	-symmetric	-symmetric	ADJ
ap-4182	282	12	hamiltonians	hamiltonian	NOUN
ap-4182	282	13	.	.	PUNCT
ap-4182	283	1	phys	phy	NOUN
ap-4182	283	2	rev	rev	VERB
ap-4182	283	3	b	b	PROPN
ap-4182	283	4	84:153101	84:153101	NUM
ap-4182	283	5	,	,	PUNCT
ap-4182	283	6	2011	2011	NUM
ap-4182	283	7	.	.	PUNCT
ap-4182	284	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	284	2	/	/	SYM
ap-4182	284	3	physrevb.84.153101	physrevb.84.153101	NOUN
ap-4182	284	4	.	.	PUNCT
ap-4182	285	1	[	[	X
ap-4182	285	2	27	27	NUM
ap-4182	285	3	]	]	PUNCT
ap-4182	285	4	k.	k.	PROPN
ap-4182	285	5	esaki	esaki	PROPN
ap-4182	285	6	,	,	PUNCT
ap-4182	285	7	m.	m.	NOUN
ap-4182	285	8	sato	sato	PROPN
ap-4182	285	9	,	,	PUNCT
ap-4182	285	10	k.	k.	PROPN
ap-4182	285	11	hasebe	hasebe	PROPN
ap-4182	285	12	,	,	PUNCT
ap-4182	285	13	m.	m.	NOUN
ap-4182	285	14	kohmoto	kohmoto	PROPN
ap-4182	285	15	.	.	PUNCT
ap-4182	286	1	edge	edge	PROPN
ap-4182	286	2	states	state	NOUN
ap-4182	286	3	and	and	CCONJ
ap-4182	286	4	topological	topological	ADJ
ap-4182	286	5	phases	phase	NOUN
ap-4182	286	6	in	in	ADP
ap-4182	286	7	non	non	ADJ
ap-4182	286	8	-	-	ADJ
ap-4182	286	9	hermitian	hermitian	ADJ
ap-4182	286	10	systems	system	NOUN
ap-4182	286	11	.	.	PUNCT
ap-4182	287	1	phys	phy	NOUN
ap-4182	287	2	rev	rev	VERB
ap-4182	287	3	b	b	PROPN
ap-4182	287	4	84:205128	84:205128	PROPN
ap-4182	287	5	,	,	PUNCT
ap-4182	287	6	2011	2011	NUM
ap-4182	287	7	.	.	PUNCT
ap-4182	288	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	288	2	/	/	SYM
ap-4182	288	3	physrevb.84.205128	physrevb.84.205128	NOUN
ap-4182	288	4	.	.	PUNCT
ap-4182	289	1	[	[	X
ap-4182	289	2	28	28	NUM
ap-4182	289	3	]	]	X
ap-4182	289	4	c.	c.	PROPN
ap-4182	289	5	yuce	yuce	PROPN
ap-4182	289	6	.	.	PUNCT
ap-4182	290	1	topological	topological	ADJ
ap-4182	290	2	phase	phase	NOUN
ap-4182	290	3	in	in	ADP
ap-4182	290	4	a	a	DET
ap-4182	290	5	non	non	ADJ
ap-4182	290	6	-	-	ADJ
ap-4182	290	7	hermitian	hermitian	ADJ
ap-4182	290	8	symmetric	symmetric	ADJ
ap-4182	290	9	system	system	NOUN
ap-4182	290	10	.	.	PUNCT
ap-4182	291	1	phys	phy	NOUN
ap-4182	291	2	lett	lett	VERB
ap-4182	291	3	a	a	DET
ap-4182	291	4	379(18–19):1213	379(18–19):1213	NUM
ap-4182	291	5	–	–	PUNCT
ap-4182	291	6	1218	1218	NUM
ap-4182	291	7	,	,	PUNCT
ap-4182	291	8	2015	2015	NUM
ap-4182	291	9	.	.	PUNCT
ap-4182	292	1	doi:10.1016	doi:10.1016	PROPN
ap-4182	292	2	/	/	SYM
ap-4182	292	3	j.physleta.2015.02.011	j.physleta.2015.02.011	PROPN
ap-4182	292	4	.	.	PUNCT
ap-4182	293	1	[	[	X
ap-4182	293	2	29	29	NUM
ap-4182	293	3	]	]	X
ap-4182	293	4	c.	c.	PROPN
ap-4182	293	5	yuce	yuce	PROPN
ap-4182	293	6	.	.	PUNCT
ap-4182	294	1	pt	pt	PROPN
ap-4182	294	2	symmetric	symmetric	ADJ
ap-4182	294	3	floquet	floquet	PROPN
ap-4182	294	4	topological	topological	ADJ
ap-4182	294	5	phase	phase	NOUN
ap-4182	294	6	.	.	PUNCT
ap-4182	295	1	eur	eur	PROPN
ap-4182	295	2	phys	phy	NOUN
ap-4182	295	3	j	j	PROPN
ap-4182	296	1	d	d	PROPN
ap-4182	296	2	69(7):184	69(7):184	PROPN
ap-4182	296	3	,	,	PUNCT
ap-4182	296	4	2015	2015	NUM
ap-4182	296	5	.	.	PUNCT
ap-4182	297	1	doi:10.1140	doi:10.1140	NOUN
ap-4182	297	2	/	/	SYM
ap-4182	297	3	epjd	epjd	PROPN
ap-4182	297	4	/	/	SYM
ap-4182	297	5	e2015	e2015	PROPN
ap-4182	297	6	-	-	PUNCT
ap-4182	297	7	60220	60220	NUM
ap-4182	297	8	-	-	SYM
ap-4182	297	9	7	7	NUM
ap-4182	297	10	.	.	PUNCT
ap-4182	298	1	[	[	X
ap-4182	298	2	30	30	NUM
ap-4182	298	3	]	]	X
ap-4182	298	4	c.	c.	NOUN
ap-4182	298	5	yuce	yuce	PROPN
ap-4182	298	6	.	.	PUNCT
ap-4182	299	1	majorana	majorana	PROPN
ap-4182	299	2	edge	edge	PROPN
ap-4182	299	3	modes	mode	NOUN
ap-4182	299	4	with	with	ADP
ap-4182	299	5	gain	gain	NOUN
ap-4182	299	6	and	and	CCONJ
ap-4182	299	7	loss	loss	NOUN
ap-4182	299	8	.	.	PUNCT
ap-4182	300	1	phys	phy	NOUN
ap-4182	300	2	rev	rev	VERB
ap-4182	300	3	a	a	DET
ap-4182	300	4	93:062130	93:062130	NUM
ap-4182	300	5	,	,	PUNCT
ap-4182	300	6	2016	2016	NUM
ap-4182	300	7	.	.	PUNCT
ap-4182	301	1	doi:10.1103	doi:10.1103	SYM
ap-4182	301	2	/	/	SYM
ap-4182	301	3	physreva.93.062130	physreva.93.062130	ADJ
ap-4182	301	4	.	.	PUNCT
ap-4182	302	1	[	[	X
ap-4182	302	2	31	31	NUM
ap-4182	302	3	]	]	PUNCT
ap-4182	302	4	m.	m.	NOUN
ap-4182	302	5	klett	klett	PROPN
ap-4182	302	6	,	,	PUNCT
ap-4182	302	7	h.	h.	PROPN
ap-4182	302	8	cartarius	cartarius	PROPN
ap-4182	302	9	,	,	PUNCT
ap-4182	302	10	d.	d.	PROPN
ap-4182	302	11	dast	dast	PROPN
ap-4182	302	12	,	,	PUNCT
ap-4182	302	13	et	et	PROPN
ap-4182	302	14	al	al	PROPN
ap-4182	302	15	.	.	PUNCT
ap-4182	302	16	relation	relation	NOUN
ap-4182	302	17	between	between	ADP
ap-4182	302	18	pt	pt	PROPN
ap-4182	302	19	-symmetry	-symmetry	NOUN
ap-4182	302	20	breaking	breaking	NOUN
ap-4182	302	21	and	and	CCONJ
ap-4182	302	22	topologically	topologically	ADV
ap-4182	302	23	nontrivial	nontrivial	ADJ
ap-4182	302	24	phases	phase	NOUN
ap-4182	302	25	in	in	ADP
ap-4182	302	26	the	the	DET
ap-4182	302	27	su	su	NOUN
ap-4182	302	28	-	-	PUNCT
ap-4182	302	29	schrieffer	schrieffer	NOUN
ap-4182	302	30	-	-	PUNCT
ap-4182	302	31	heeger	heeger	NOUN
ap-4182	302	32	and	and	CCONJ
ap-4182	302	33	kitaev	kitaev	NOUN
ap-4182	302	34	models	model	NOUN
ap-4182	302	35	.	.	PUNCT
ap-4182	303	1	phys	phy	NOUN
ap-4182	303	2	rev	rev	VERB
ap-4182	303	3	a	a	DET
ap-4182	303	4	95:053626	95:053626	NUM
ap-4182	303	5	,	,	PUNCT
ap-4182	303	6	2017	2017	NUM
ap-4182	303	7	.	.	PUNCT
ap-4182	304	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	304	2	/	/	SYM
ap-4182	304	3	physreva.95.053626	physreva.95.053626	NOUN
ap-4182	304	4	.	.	PUNCT
ap-4182	305	1	[	[	X
ap-4182	305	2	32	32	NUM
ap-4182	305	3	]	]	PUNCT
ap-4182	305	4	h.	h.	PROPN
ap-4182	305	5	schomerus	schomerus	PROPN
ap-4182	305	6	.	.	PUNCT
ap-4182	306	1	topologically	topologically	PROPN
ap-4182	306	2	protected	protect	VERB
ap-4182	306	3	midgap	midgap	PROPN
ap-4182	306	4	states	state	NOUN
ap-4182	306	5	in	in	ADP
ap-4182	306	6	complex	complex	ADJ
ap-4182	306	7	photonic	photonic	ADJ
ap-4182	306	8	lattices	lattice	NOUN
ap-4182	306	9	.	.	PUNCT
ap-4182	307	1	opt	opt	PROPN
ap-4182	307	2	lett	lett	PROPN
ap-4182	307	3	38(11):1912–1914	38(11):1912–1914	PROPN
ap-4182	307	4	,	,	PUNCT
ap-4182	307	5	2013	2013	NUM
ap-4182	307	6	.	.	PUNCT
ap-4182	308	1	doi:10.1364	doi:10.1364	NOUN
ap-4182	308	2	/	/	SYM
ap-4182	308	3	ol.38.001912	ol.38.001912	ADJ
ap-4182	308	4	.	.	PUNCT
ap-4182	309	1	[	[	X
ap-4182	309	2	33	33	NUM
ap-4182	309	3	]	]	PUNCT
ap-4182	309	4	j.	j.	PROPN
ap-4182	309	5	m.	m.	PROPN
ap-4182	309	6	zeuner	zeuner	PROPN
ap-4182	309	7	,	,	PUNCT
ap-4182	309	8	m.	m.	NOUN
ap-4182	309	9	c.	c.	PROPN
ap-4182	309	10	rechtsman	rechtsman	NOUN
ap-4182	309	11	,	,	PUNCT
ap-4182	309	12	y.	y.	PROPN
ap-4182	309	13	plotnik	plotnik	PROPN
ap-4182	309	14	,	,	PUNCT
ap-4182	309	15	et	et	PROPN
ap-4182	309	16	al	al	PROPN
ap-4182	309	17	.	.	PUNCT
ap-4182	309	18	observation	observation	NOUN
ap-4182	309	19	of	of	ADP
ap-4182	309	20	a	a	DET
ap-4182	309	21	topological	topological	ADJ
ap-4182	309	22	transition	transition	NOUN
ap-4182	309	23	in	in	ADP
ap-4182	309	24	the	the	DET
ap-4182	309	25	bulk	bulk	NOUN
ap-4182	309	26	of	of	ADP
ap-4182	309	27	a	a	DET
ap-4182	309	28	non	non	ADJ
ap-4182	309	29	-	-	ADJ
ap-4182	309	30	hermitian	hermitian	ADJ
ap-4182	309	31	system	system	NOUN
ap-4182	309	32	.	.	PUNCT
ap-4182	310	1	phys	phy	NOUN
ap-4182	310	2	rev	rev	VERB
ap-4182	310	3	lett	lett	PROPN
ap-4182	310	4	115:040402	115:040402	PROPN
ap-4182	310	5	,	,	PUNCT
ap-4182	310	6	2015	2015	NUM
ap-4182	310	7	.	.	PUNCT
ap-4182	311	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	311	2	/	/	SYM
ap-4182	311	3	physrevlett.115.040402	physrevlett.115.040402	NOUN
ap-4182	311	4	.	.	PUNCT
ap-4182	312	1	[	[	X
ap-4182	312	2	34	34	NUM
ap-4182	312	3	]	]	PUNCT
ap-4182	312	4	x.	x.	NOUN
ap-4182	312	5	wang	wang	PROPN
ap-4182	312	6	,	,	PUNCT
ap-4182	312	7	t.	t.	PROPN
ap-4182	312	8	liu	liu	PROPN
ap-4182	312	9	,	,	PUNCT
ap-4182	312	10	y.	y.	PROPN
ap-4182	312	11	xiong	xiong	PROPN
ap-4182	312	12	,	,	PUNCT
ap-4182	312	13	p.	p.	PROPN
ap-4182	312	14	tong	tong	PROPN
ap-4182	312	15	.	.	PUNCT
ap-4182	313	1	spontaneous	spontaneous	ADJ
ap-4182	313	2	pt	pt	PROPN
ap-4182	313	3	-symmetry	-symmetry	NOUN
ap-4182	313	4	breaking	break	VERB
ap-4182	313	5	in	in	ADP
ap-4182	313	6	non	non	ADJ
ap-4182	313	7	-	-	ADJ
ap-4182	313	8	hermitian	hermitian	ADJ
ap-4182	313	9	kitaev	kitaev	NOUN
ap-4182	313	10	and	and	CCONJ
ap-4182	313	11	extended	extended	ADJ
ap-4182	313	12	kitaev	kitaev	NOUN
ap-4182	313	13	models	model	NOUN
ap-4182	313	14	.	.	PUNCT
ap-4182	314	1	phys	phy	NOUN
ap-4182	314	2	rev	rev	VERB
ap-4182	314	3	a	a	DET
ap-4182	314	4	92:012116	92:012116	NUM
ap-4182	314	5	,	,	PUNCT
ap-4182	314	6	2015	2015	NUM
ap-4182	314	7	.	.	PUNCT
ap-4182	315	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	315	2	/	/	SYM
ap-4182	315	3	physreva.92.012116	physreva.92.012116	ADJ
ap-4182	315	4	.	.	PUNCT
ap-4182	316	1	[	[	X
ap-4182	316	2	35	35	NUM
ap-4182	316	3	]	]	X
ap-4182	316	4	s.	s.	PROPN
ap-4182	316	5	weimann	weimann	PROPN
ap-4182	316	6	,	,	PUNCT
ap-4182	316	7	m.	m.	NOUN
ap-4182	316	8	kremer	kremer	PROPN
ap-4182	316	9	,	,	PUNCT
ap-4182	316	10	y.	y.	PROPN
ap-4182	316	11	plotnik	plotnik	PROPN
ap-4182	316	12	,	,	PUNCT
ap-4182	316	13	et	et	PROPN
ap-4182	316	14	al	al	PROPN
ap-4182	316	15	.	.	PUNCT
ap-4182	316	16	topologically	topologically	PROPN
ap-4182	316	17	protected	protect	VERB
ap-4182	316	18	bound	bind	VERB
ap-4182	316	19	states	state	NOUN
ap-4182	316	20	in	in	ADP
ap-4182	316	21	photonic	photonic	ADJ
ap-4182	316	22	parity	parity	NOUN
ap-4182	316	23	-	-	PUNCT
ap-4182	316	24	time	time	NOUN
ap-4182	316	25	-	-	PUNCT
ap-4182	316	26	symmetric	symmetric	ADJ
ap-4182	316	27	crystals	crystal	NOUN
ap-4182	316	28	.	.	PUNCT
ap-4182	317	1	nat	nat	NOUN
ap-4182	317	2	mater	mater	NOUN
ap-4182	317	3	16(4):433–438	16(4):433–438	NUM
ap-4182	317	4	,	,	PUNCT
ap-4182	317	5	2017	2017	NUM
ap-4182	317	6	.	.	PUNCT
ap-4182	318	1	doi:10.1038	doi:10.1038	NOUN
ap-4182	318	2	/	/	SYM
ap-4182	318	3	nmat4811	nmat4811	PROPN
ap-4182	318	4	.	.	PUNCT
ap-4182	319	1	475	475	NUM
ap-4182	319	2	http://dx.doi.org/10.1103/physrevb.92.195107	http://dx.doi.org/10.1103/physrevb.92.195107	PROPN
ap-4182	319	3	http://dx.doi.org/10.1088/1367-2630/15/8/085001	http://dx.doi.org/10.1088/1367-2630/15/8/085001	PROPN
ap-4182	319	4	http://dx.doi.org/10.1038/srep21427	http://dx.doi.org/10.1038/srep21427	ADJ
ap-4182	319	5	http://dx.doi.org/10.1103/physrevlett.80.5243	http://dx.doi.org/10.1103/physrevlett.80.5243	NOUN
ap-4182	319	6	http://dx.doi.org/10.1016/s0375-9601(01)00301-2	http://dx.doi.org/10.1016/s0375-9601(01)00301-2	PROPN
ap-4182	319	7	http://dx.doi.org/10.1103/physrevlett.89.270401	http://dx.doi.org/10.1103/physrevlett.89.270401	PROPN
ap-4182	319	8	http://dx.doi.org/10.1016/j.physleta.2011.08.005	http://dx.doi.org/10.1016/j.physleta.2011.08.005	VERB
ap-4182	319	9	http://dx.doi.org/10.1088/1751-8113/43/5/055307	http://dx.doi.org/10.1088/1751-8113/43/5/055307	PROPN
ap-4182	319	10	http://dx.doi.org/10.1088/1751-8113/45/44/444021	http://dx.doi.org/10.1088/1751-8113/45/44/444021	NOUN
ap-4182	319	11	http://dx.doi.org/10.1088/1751-8113/43/14/145301	http://dx.doi.org/10.1088/1751-8113/43/14/145301	NOUN
ap-4182	319	12	http://dx.doi.org/10.1007/s10582-005-0115-x	http://dx.doi.org/10.1007/s10582-005-0115-x	VERB
ap-4182	319	13	http://dx.doi.org/10.1088/0305-4470/35/41/311	http://dx.doi.org/10.1088/0305-4470/35/41/311	NOUN
ap-4182	319	14	http://dx.doi.org/10.1007/s10773-014-2467-0	http://dx.doi.org/10.1007/s10773-014-2467-0	SYM
ap-4182	320	1	http://dx.doi.org/10.1088/0305-4470/39/43/008	http://dx.doi.org/10.1088/0305-4470/39/43/008	VERB
ap-4182	321	1	http://dx.doi.org/10.1103/physrevd.78.065032	http://dx.doi.org/10.1103/physrevd.78.065032	PROPN
ap-4182	321	2	http://dx.doi.org/10.1103/physrevlett.101.150408	http://dx.doi.org/10.1103/physrevlett.101.150408	PROPN
ap-4182	321	3	http://dx.doi.org/10.1088/1751-8113/41/25/255206	http://dx.doi.org/10.1088/1751-8113/41/25/255206	ADP
ap-4182	321	4	http://dx.doi.org/10.1088/1751-8113/41/24/244019	http://dx.doi.org/10.1088/1751-8113/41/24/244019	PART
ap-4182	321	5	http://dx.doi.org/10.1088/1751-8113/46/27/275307	http://dx.doi.org/10.1088/1751-8113/46/27/275307	X
ap-4182	321	6	http://dx.doi.org/10.1103/physreva.90.052120	http://dx.doi.org/10.1103/physreva.90.052120	PROPN
ap-4182	321	7	http://dx.doi.org/10.1088/1751-8113/48/33/335302	http://dx.doi.org/10.1088/1751-8113/48/33/335302	X
ap-4182	322	1	http://dx.doi.org/10.1103/physrevb.84.153101	http://dx.doi.org/10.1103/physrevb.84.153101	PROPN
ap-4182	322	2	http://dx.doi.org/10.1103/physrevb.84.205128	http://dx.doi.org/10.1103/physrevb.84.205128	VERB
ap-4182	322	3	http://dx.doi.org/10.1016/j.physleta.2015.02.011	http://dx.doi.org/10.1016/j.physleta.2015.02.011	PROPN
ap-4182	322	4	http://dx.doi.org/10.1140/epjd/e2015-60220-7	http://dx.doi.org/10.1140/epjd/e2015-60220-7	VERB
ap-4182	322	5	http://dx.doi.org/10.1103/physreva.93.062130	http://dx.doi.org/10.1103/physreva.93.062130	PROPN
ap-4182	322	6	http://dx.doi.org/10.1103/physreva.95.053626	http://dx.doi.org/10.1103/physreva.95.053626	ADJ
ap-4182	323	1	http://dx.doi.org/10.1364/ol.38.001912	http://dx.doi.org/10.1364/ol.38.001912	ADJ
ap-4182	323	2	http://dx.doi.org/10.1103/physrevlett.115.040402	http://dx.doi.org/10.1103/physrevlett.115.040402	NOUN
ap-4182	324	1	http://dx.doi.org/10.1103/physreva.92.012116	http://dx.doi.org/10.1103/physreva.92.012116	PROPN
ap-4182	325	1	http://dx.doi.org/10.1038/nmat4811	http://dx.doi.org/10.1038/nmat4811	PROPN
ap-4182	326	1	m.	m.	PROPN
ap-4182	326	2	wagner	wagner	PROPN
ap-4182	326	3	,	,	PUNCT
ap-4182	326	4	f.	f.	PROPN
ap-4182	326	5	dangel	dangel	PROPN
ap-4182	326	6	,	,	PUNCT
ap-4182	326	7	h.	h.	PROPN
ap-4182	326	8	cartarius	cartarius	PROPN
ap-4182	326	9	et	et	PROPN
ap-4182	326	10	al	al	PROPN
ap-4182	326	11	.	.	PROPN
ap-4182	327	1	acta	acta	PROPN
ap-4182	327	2	polytechnica	polytechnica	PROPN
ap-4182	328	1	[	[	X
ap-4182	328	2	36	36	NUM
ap-4182	328	3	]	]	PUNCT
ap-4182	329	1	j.	j.	PROPN
ap-4182	329	2	zak	zak	PROPN
ap-4182	329	3	.	.	PUNCT
ap-4182	330	1	berry	berry	VERB
ap-4182	330	2	’s	’s	PART
ap-4182	330	3	phase	phase	NOUN
ap-4182	330	4	for	for	ADP
ap-4182	330	5	energy	energy	NOUN
ap-4182	330	6	bands	band	NOUN
ap-4182	330	7	in	in	ADP
ap-4182	330	8	solids	solid	NOUN
ap-4182	330	9	.	.	PUNCT
ap-4182	331	1	phys	phy	NOUN
ap-4182	331	2	rev	rev	VERB
ap-4182	331	3	lett	lett	PROPN
ap-4182	331	4	62:2747–2750	62:2747–2750	PROPN
ap-4182	331	5	,	,	PUNCT
ap-4182	331	6	1989	1989	NUM
ap-4182	331	7	.	.	PUNCT
ap-4182	332	1	doi:10.1103	doi:10.1103	NOUN
ap-4182	332	2	/	/	SYM
ap-4182	332	3	physrevlett.62.2747	physrevlett.62.2747	NOUN
ap-4182	332	4	.	.	PUNCT
ap-4182	333	1	[	[	X
ap-4182	333	2	37	37	NUM
ap-4182	333	3	]	]	PUNCT
ap-4182	333	4	s.-d	s.-d	PROPN
ap-4182	333	5	.	.	PUNCT
ap-4182	334	1	liang	liang	PROPN
ap-4182	334	2	,	,	PUNCT
ap-4182	334	3	g.-y	g.-y	PROPN
ap-4182	334	4	.	.	PUNCT
ap-4182	335	1	huang	huang	PROPN
ap-4182	335	2	.	.	PUNCT
ap-4182	336	1	topological	topological	PROPN
ap-4182	336	2	invariance	invariance	PROPN
ap-4182	336	3	and	and	CCONJ
ap-4182	336	4	global	global	ADJ
ap-4182	336	5	berry	berry	NOUN
ap-4182	336	6	phase	phase	NOUN
ap-4182	336	7	in	in	ADP
ap-4182	336	8	non	non	ADJ
ap-4182	336	9	-	-	ADJ
ap-4182	336	10	hermitian	hermitian	ADJ
ap-4182	336	11	systems	system	NOUN
ap-4182	336	12	.	.	PUNCT
ap-4182	337	1	phys	phy	NOUN
ap-4182	337	2	rev	rev	VERB
ap-4182	337	3	a	a	DET
ap-4182	337	4	87:012118	87:012118	NUM
ap-4182	337	5	,	,	PUNCT
ap-4182	337	6	2013	2013	NUM
ap-4182	337	7	.	.	PUNCT
ap-4182	338	1	doi:10.1103	doi:10.1103	PROPN
ap-4182	338	2	/	/	SYM
ap-4182	338	3	physreva.87.012118	physreva.87.012118	PROPN
ap-4182	338	4	.	.	PUNCT
ap-4182	339	1	[	[	X
ap-4182	339	2	38	38	NUM
ap-4182	339	3	]	]	PUNCT
ap-4182	339	4	i.	i.	PROPN
ap-4182	339	5	mandal	mandal	PROPN
ap-4182	339	6	,	,	PUNCT
ap-4182	339	7	s.	s.	PROPN
ap-4182	339	8	tewari	tewari	PROPN
ap-4182	339	9	.	.	PUNCT
ap-4182	340	1	exceptional	exceptional	ADJ
ap-4182	340	2	point	point	NOUN
ap-4182	340	3	description	description	NOUN
ap-4182	340	4	of	of	ADP
ap-4182	340	5	one	one	NUM
ap-4182	340	6	-	-	PUNCT
ap-4182	340	7	dimensional	dimensional	ADJ
ap-4182	340	8	chiral	chiral	ADJ
ap-4182	340	9	topological	topological	ADJ
ap-4182	340	10	superconductors	superconductor	NOUN
ap-4182	340	11	/	/	SYM
ap-4182	340	12	superfluids	superfluids	PROPN
ap-4182	340	13	in	in	ADP
ap-4182	340	14	bdi	bdi	PROPN
ap-4182	340	15	class	class	PROPN
ap-4182	340	16	.	.	PUNCT
ap-4182	341	1	physica	physica	NOUN
ap-4182	341	2	e	e	PROPN
ap-4182	341	3	79:180	79:180	PROPN
ap-4182	341	4	–	–	PUNCT
ap-4182	341	5	187	187	NUM
ap-4182	341	6	,	,	PUNCT
ap-4182	341	7	2016	2016	NUM
ap-4182	341	8	.	.	PUNCT
ap-4182	342	1	doi:10.1016	doi:10.1016	PROPN
ap-4182	342	2	/	/	SYM
ap-4182	342	3	j.physe.2015.12.009	j.physe.2015.12.009	PROPN
ap-4182	342	4	.	.	PUNCT
ap-4182	343	1	[	[	X
ap-4182	343	2	39	39	NUM
ap-4182	343	3	]	]	PUNCT
ap-4182	343	4	d.	d.	PROPN
ap-4182	343	5	c.	c.	PROPN
ap-4182	343	6	brody	brody	PROPN
ap-4182	343	7	.	.	PUNCT
ap-4182	344	1	biorthogonal	biorthogonal	ADJ
ap-4182	344	2	quantum	quantum	ADJ
ap-4182	344	3	mechanics	mechanic	NOUN
ap-4182	344	4	.	.	PUNCT
ap-4182	345	1	j	j	PROPN
ap-4182	345	2	phys	phy	NOUN
ap-4182	345	3	a	a	DET
ap-4182	345	4	47(3):035305	47(3):035305	NUM
ap-4182	345	5	,	,	PUNCT
ap-4182	345	6	2014	2014	NUM
ap-4182	345	7	.	.	PUNCT
ap-4182	346	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-4182	346	2	-	-	PUNCT
ap-4182	346	3	8113/47/3/035305	8113/47/3/035305	NUM
ap-4182	346	4	.	.	PUNCT
ap-4182	347	1	[	[	X
ap-4182	347	2	40	40	NUM
ap-4182	347	3	]	]	X
ap-4182	347	4	n.	n.	PROPN
ap-4182	347	5	moiseyev	moiseyev	PROPN
ap-4182	347	6	.	.	PUNCT
ap-4182	348	1	non	non	ADJ
ap-4182	348	2	-	-	ADJ
ap-4182	348	3	hermitian	hermitian	ADJ
ap-4182	348	4	quantum	quantum	ADJ
ap-4182	348	5	mechanics	mechanic	NOUN
ap-4182	348	6	.	.	PUNCT
ap-4182	349	1	cambridge	cambridge	PROPN
ap-4182	349	2	university	university	PROPN
ap-4182	349	3	press	press	PROPN
ap-4182	349	4	,	,	PUNCT
ap-4182	349	5	cambridge	cambridge	PROPN
ap-4182	349	6	,	,	PUNCT
ap-4182	349	7	2011	2011	NUM
ap-4182	349	8	.	.	PUNCT
ap-4182	350	1	[	[	X
ap-4182	350	2	41	41	NUM
ap-4182	350	3	]	]	X
ap-4182	350	4	w.	w.	PROPN
ap-4182	350	5	p.	p.	PROPN
ap-4182	350	6	su	su	PROPN
ap-4182	350	7	,	,	PUNCT
ap-4182	350	8	j.	j.	PROPN
ap-4182	350	9	r.	r.	PROPN
ap-4182	350	10	schrieffer	schrieffer	PROPN
ap-4182	350	11	,	,	PUNCT
ap-4182	350	12	a.	a.	PROPN
ap-4182	350	13	j.	j.	PROPN
ap-4182	350	14	heeger	heeger	PROPN
ap-4182	350	15	.	.	PUNCT
ap-4182	351	1	solitons	soliton	NOUN
ap-4182	351	2	in	in	ADP
ap-4182	351	3	polyacetylene	polyacetylene	NOUN
ap-4182	351	4	.	.	PUNCT
ap-4182	352	1	phys	phy	NOUN
ap-4182	352	2	rev	rev	VERB
ap-4182	352	3	lett	lett	PROPN
ap-4182	352	4	42:1698–1701	42:1698–1701	PROPN
ap-4182	352	5	,	,	PUNCT
ap-4182	352	6	1979	1979	NUM
ap-4182	352	7	.	.	PUNCT
ap-4182	353	1	doi:10.1103	doi:10.1103	PROPN
ap-4182	353	2	/	/	SYM
ap-4182	353	3	physrevlett.42.1698	physrevlett.42.1698	NOUN
ap-4182	353	4	.	.	PUNCT
ap-4182	354	1	[	[	X
ap-4182	354	2	42	42	NUM
ap-4182	354	3	]	]	X
ap-4182	354	4	m.	m.	NOUN
ap-4182	354	5	v.	v.	ADP
ap-4182	354	6	berry	berry	PROPN
ap-4182	354	7	.	.	PUNCT
ap-4182	355	1	quantal	quantal	ADJ
ap-4182	355	2	phase	phase	NOUN
ap-4182	355	3	factors	factor	NOUN
ap-4182	355	4	accompanying	accompany	VERB
ap-4182	355	5	adiabatic	adiabatic	ADJ
ap-4182	355	6	changes	change	NOUN
ap-4182	355	7	.	.	PUNCT
ap-4182	356	1	proc	proc	NOUN
ap-4182	356	2	r	r	PROPN
ap-4182	356	3	soc	soc	PROPN
ap-4182	356	4	london	london	PROPN
ap-4182	356	5	,	,	PUNCT
ap-4182	356	6	ser	ser	NOUN
ap-4182	356	7	a	a	DET
ap-4182	356	8	392(1802):45–57	392(1802):45–57	NUM
ap-4182	356	9	,	,	PUNCT
ap-4182	356	10	1984	1984	NUM
ap-4182	356	11	.	.	PUNCT
ap-4182	357	1	doi:10.1098	doi:10.1098	PROPN
ap-4182	357	2	/	/	SYM
ap-4182	357	3	rspa.1984.0023	rspa.1984.0023	NOUN
ap-4182	357	4	.	.	PUNCT
ap-4182	358	1	[	[	X
ap-4182	358	2	43	43	NUM
ap-4182	358	3	]	]	X
ap-4182	358	4	y.	y.	PROPN
ap-4182	358	5	hatsugai	hatsugai	PROPN
ap-4182	358	6	.	.	PUNCT
ap-4182	359	1	quantized	quantize	VERB
ap-4182	359	2	berry	berry	NOUN
ap-4182	359	3	phases	phase	NOUN
ap-4182	359	4	as	as	ADP
ap-4182	359	5	a	a	DET
ap-4182	359	6	local	local	ADJ
ap-4182	359	7	order	order	NOUN
ap-4182	359	8	parameter	parameter	NOUN
ap-4182	359	9	of	of	ADP
ap-4182	359	10	a	a	DET
ap-4182	359	11	quantum	quantum	ADJ
ap-4182	359	12	liquid	liquid	NOUN
ap-4182	359	13	.	.	PUNCT
ap-4182	360	1	j	j	PROPN
ap-4182	360	2	phys	phys	PROPN
ap-4182	360	3	soc	soc	PROPN
ap-4182	360	4	jpn	jpn	PROPN
ap-4182	360	5	75(12):123601–123601	75(12):123601–123601	NUM
ap-4182	360	6	,	,	PUNCT
ap-4182	360	7	2006	2006	NUM
ap-4182	360	8	.	.	PUNCT
ap-4182	361	1	doi:10.1143	doi:10.1143	NOUN
ap-4182	361	2	/	/	SYM
ap-4182	361	3	jpsj.75.123601	jpsj.75.123601	PROPN
ap-4182	361	4	.	.	PUNCT
ap-4182	362	1	[	[	X
ap-4182	362	2	44	44	NUM
ap-4182	362	3	]	]	PUNCT
ap-4182	362	4	j.	j.	PROPN
ap-4182	362	5	c.	c.	PROPN
ap-4182	362	6	garrison	garrison	PROPN
ap-4182	362	7	,	,	PUNCT
ap-4182	362	8	e.	e.	PROPN
ap-4182	362	9	m.	m.	PROPN
ap-4182	362	10	wright	wright	PROPN
ap-4182	362	11	.	.	PUNCT
ap-4182	363	1	complex	complex	ADJ
ap-4182	363	2	geometrical	geometrical	ADJ
ap-4182	363	3	phases	phase	NOUN
ap-4182	363	4	for	for	ADP
ap-4182	363	5	dissipative	dissipative	ADJ
ap-4182	363	6	systems	system	NOUN
ap-4182	363	7	.	.	PUNCT
ap-4182	364	1	phys	phy	NOUN
ap-4182	364	2	lett	lett	VERB
ap-4182	364	3	a	a	DET
ap-4182	364	4	128(34):177–181	128(34):177–181	PROPN
ap-4182	364	5	,	,	PUNCT
ap-4182	364	6	1988	1988	NUM
ap-4182	364	7	.	.	PUNCT
ap-4182	365	1	doi:10.1016/0375	doi:10.1016/0375	VERB
ap-4182	365	2	-	-	PUNCT
ap-4182	365	3	9601(88)90905	9601(88)90905	NOUN
ap-4182	365	4	-	-	PUNCT
ap-4182	365	5	x.	x.	NOUN
ap-4182	366	1	[	[	X
ap-4182	366	2	45	45	NUM
ap-4182	366	3	]	]	PUNCT
ap-4182	366	4	b.	b.	PROPN
ap-4182	366	5	n.	n.	PROPN
ap-4182	366	6	parlett	parlett	PROPN
ap-4182	366	7	,	,	PUNCT
ap-4182	366	8	d.	d.	PROPN
ap-4182	366	9	r.	r.	PROPN
ap-4182	366	10	taylor	taylor	PROPN
ap-4182	366	11	,	,	PUNCT
ap-4182	366	12	z.	z.	PROPN
ap-4182	366	13	a.	a.	PROPN
ap-4182	366	14	liu	liu	PROPN
ap-4182	366	15	.	.	PUNCT
ap-4182	367	1	a	a	DET
ap-4182	367	2	look	look	VERB
ap-4182	367	3	-	-	PUNCT
ap-4182	367	4	ahead	ahead	NOUN
ap-4182	367	5	lanczos	lanczos	PROPN
ap-4182	367	6	algorithm	algorithm	NOUN
ap-4182	367	7	for	for	ADP
ap-4182	367	8	unsymmetric	unsymmetric	ADJ
ap-4182	367	9	matrices	matrix	NOUN
ap-4182	367	10	.	.	PUNCT
ap-4182	368	1	math	math	PROPN
ap-4182	368	2	comp	comp	PROPN
ap-4182	368	3	44(169):105–124	44(169):105–124	PROPN
ap-4182	368	4	,	,	PUNCT
ap-4182	368	5	1985	1985	NUM
ap-4182	368	6	.	.	PUNCT
ap-4182	369	1	doi:10.1090	doi:10.1090	NOUN
ap-4182	369	2	/	/	SYM
ap-4182	369	3	s0025	s0025	PROPN
ap-4182	369	4	-	-	PUNCT
ap-4182	369	5	5718	5718	NUM
ap-4182	369	6	-	-	PUNCT
ap-4182	369	7	1985	1985	NUM
ap-4182	369	8	-	-	PUNCT
ap-4182	369	9	0771034	0771034	NUM
ap-4182	369	10	-	-	SYM
ap-4182	369	11	2	2	NUM
ap-4182	369	12	.	.	X
ap-4182	369	13	476	476	NUM
ap-4182	369	14	http://dx.doi.org/10.1103/physrevlett.62.2747	http://dx.doi.org/10.1103/physrevlett.62.2747	PROPN
ap-4182	369	15	http://dx.doi.org/10.1103/physreva.87.012118	http://dx.doi.org/10.1103/physreva.87.012118	VERB
ap-4182	369	16	http://dx.doi.org/10.1016/j.physe.2015.12.009	http://dx.doi.org/10.1016/j.physe.2015.12.009	NOUN
ap-4182	369	17	http://dx.doi.org/10.1088/1751-8113/47/3/035305	http://dx.doi.org/10.1088/1751-8113/47/3/035305	PROPN
ap-4182	369	18	http://dx.doi.org/10.1103/physrevlett.42.1698	http://dx.doi.org/10.1103/physrevlett.42.1698	PROPN
ap-4182	369	19	http://dx.doi.org/10.1098/rspa.1984.0023	http://dx.doi.org/10.1098/rspa.1984.0023	NOUN
ap-4182	369	20	http://dx.doi.org/10.1143/jpsj.75.123601	http://dx.doi.org/10.1143/jpsj.75.123601	PROPN
ap-4182	369	21	http://dx.doi.org/10.1016/0375-9601(88)90905-x	http://dx.doi.org/10.1016/0375-9601(88)90905-x	PROPN
ap-4182	369	22	http://dx.doi.org/10.1090/s0025-5718-1985-0771034-2	http://dx.doi.org/10.1090/s0025-5718-1985-0771034-2	NUM
ap-4182	369	23	acta	acta	PROPN
ap-4182	369	24	polytechnica	polytechnica	PROPN
ap-4182	369	25	57(6):470–476	57(6):470–476	PROPN
ap-4182	369	26	,	,	PUNCT
ap-4182	369	27	2017	2017	NUM
ap-4182	369	28	1	1	NUM
ap-4182	369	29	introduction	introduction	NOUN
ap-4182	369	30	2	2	NUM
ap-4182	369	31	complex	complex	ADJ
ap-4182	369	32	berry	berry	NOUN
ap-4182	369	33	phase	phase	NOUN
ap-4182	369	34	3	3	NUM
ap-4182	369	35	numerical	numerical	ADJ
ap-4182	369	36	gauge	gauge	NOUN
ap-4182	369	37	smoothing	smooth	VERB
ap-4182	369	38	4	4	NUM
ap-4182	369	39	application	application	NOUN
ap-4182	369	40	to	to	ADP
ap-4182	369	41	a	a	DET
ap-4182	369	42	one	one	NUM
ap-4182	369	43	-	-	PUNCT
ap-4182	369	44	dimensional	dimensional	ADJ
ap-4182	369	45	lattice	lattice	NOUN
ap-4182	369	46	system	system	NOUN
ap-4182	369	47	5	5	NUM
ap-4182	369	48	conclusion	conclusion	NOUN
ap-4182	369	49	references	reference	NOUN