Majorana charges, winding numbers and Chern numbers in quantum Ising models

Abstract Mapping a many-body state on a loop in parameter space is a simple way to characterize a quantum state. The connections of such a geometrical representation to the concepts of Chern number and Majorana zero mode are investigated based on a generalized quantum spin system with short and long...

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Autores principales:	G. Zhang, C. Li, Z. Song
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/7590c88317db40f5a02a6fcd53cfd5c0
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spelling	oai:doaj.org-article:7590c88317db40f5a02a6fcd53cfd5c02021-12-02T16:06:51ZMajorana charges, winding numbers and Chern numbers in quantum Ising models10.1038/s41598-017-08323-02045-2322https://doaj.org/article/7590c88317db40f5a02a6fcd53cfd5c02017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-08323-0https://doaj.org/toc/2045-2322Abstract Mapping a many-body state on a loop in parameter space is a simple way to characterize a quantum state. The connections of such a geometrical representation to the concepts of Chern number and Majorana zero mode are investigated based on a generalized quantum spin system with short and long-range interactions. We show that the topological invariants, the Chern numbers of corresponding Bloch band, is equivalent to the winding number in the auxiliary plane, which can be utilized to characterize the phase diagram. We introduce the concept of Majorana charge, the magnitude of which is defined by the distribution of Majorana fermion probability in zero-mode states, and the sign is defined by the type of Majorana fermion. By direct calculations of the Majorana modes we analytically and numerically verify that the Majorana charge is equal to Chern numbers and winding numbers.G. ZhangC. LiZ. SongNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-13 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q G. Zhang C. Li Z. Song Majorana charges, winding numbers and Chern numbers in quantum Ising models
description	Abstract Mapping a many-body state on a loop in parameter space is a simple way to characterize a quantum state. The connections of such a geometrical representation to the concepts of Chern number and Majorana zero mode are investigated based on a generalized quantum spin system with short and long-range interactions. We show that the topological invariants, the Chern numbers of corresponding Bloch band, is equivalent to the winding number in the auxiliary plane, which can be utilized to characterize the phase diagram. We introduce the concept of Majorana charge, the magnitude of which is defined by the distribution of Majorana fermion probability in zero-mode states, and the sign is defined by the type of Majorana fermion. By direct calculations of the Majorana modes we analytically and numerically verify that the Majorana charge is equal to Chern numbers and winding numbers.
format	article
author	G. Zhang C. Li Z. Song
author_facet	G. Zhang C. Li Z. Song
author_sort	G. Zhang
title	Majorana charges, winding numbers and Chern numbers in quantum Ising models
title_short	Majorana charges, winding numbers and Chern numbers in quantum Ising models
title_full	Majorana charges, winding numbers and Chern numbers in quantum Ising models
title_fullStr	Majorana charges, winding numbers and Chern numbers in quantum Ising models
title_full_unstemmed	Majorana charges, winding numbers and Chern numbers in quantum Ising models
title_sort	majorana charges, winding numbers and chern numbers in quantum ising models
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/7590c88317db40f5a02a6fcd53cfd5c0
work_keys_str_mv	AT gzhang majoranachargeswindingnumbersandchernnumbersinquantumisingmodels AT cli majoranachargeswindingnumbersandchernnumbersinquantumisingmodels AT zsong majoranachargeswindingnumbersandchernnumbersinquantumisingmodels
_version_	1718384849319886848

Majorana charges, winding numbers and Chern numbers in quantum Ising models

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