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Exactly solvable spin chain models corresponding to BDI class of topological superconductors

We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, n(M) which are in turn related to an integer winding number, n(W). The present class of...

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Autores principales: Jafari, S. A., Shahbazi, Farhad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5011742/
https://www.ncbi.nlm.nih.gov/pubmed/27596804
http://dx.doi.org/10.1038/srep32720
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author Jafari, S. A.
Shahbazi, Farhad
author_facet Jafari, S. A.
Shahbazi, Farhad
author_sort Jafari, S. A.
collection PubMed
description We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, n(M) which are in turn related to an integer winding number, n(W). The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions – a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the n(W) (n(M)) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.
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spelling pubmed-50117422016-09-12 Exactly solvable spin chain models corresponding to BDI class of topological superconductors Jafari, S. A. Shahbazi, Farhad Sci Rep Article We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, n(M) which are in turn related to an integer winding number, n(W). The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions – a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the n(W) (n(M)) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well. Nature Publishing Group 2016-09-06 /pmc/articles/PMC5011742/ /pubmed/27596804 http://dx.doi.org/10.1038/srep32720 Text en Copyright © 2016, The Author(s) http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Jafari, S. A.
Shahbazi, Farhad
Exactly solvable spin chain models corresponding to BDI class of topological superconductors
title Exactly solvable spin chain models corresponding to BDI class of topological superconductors
title_full Exactly solvable spin chain models corresponding to BDI class of topological superconductors
title_fullStr Exactly solvable spin chain models corresponding to BDI class of topological superconductors
title_full_unstemmed Exactly solvable spin chain models corresponding to BDI class of topological superconductors
title_short Exactly solvable spin chain models corresponding to BDI class of topological superconductors
title_sort exactly solvable spin chain models corresponding to bdi class of topological superconductors
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5011742/
https://www.ncbi.nlm.nih.gov/pubmed/27596804
http://dx.doi.org/10.1038/srep32720
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