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ℤ(3) parafermionic chain emerging from Yang-Baxter equation

We construct the 1D [Image: see text] parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the [Image: see text] parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding numb...

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Detalles Bibliográficos
Autores principales: Yu, Li-Wei, Ge, Mo-Lin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4794089/
https://www.ncbi.nlm.nih.gov/pubmed/26902999
http://dx.doi.org/10.1038/srep21497
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author Yu, Li-Wei
Ge, Mo-Lin
author_facet Yu, Li-Wei
Ge, Mo-Lin
author_sort Yu, Li-Wei
collection PubMed
description We construct the 1D [Image: see text] parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the [Image: see text] parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the [Image: see text] parafermionic model is a direct generalization of 1D [Image: see text] Kitaev model. Both the [Image: see text] and [Image: see text] model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian [Image: see text] based on Yang-Baxter equation. Different from the Majorana doubling, the [Image: see text] holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P[Image: see text] and emergent parafermionic operator Γ, which are the generalizations of parity P(M) and emergent Majorana operator in Lee-Wilczek model, respectively. Both the [Image: see text] parafermionic model and [Image: see text] can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.
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spelling pubmed-47940892016-03-17 ℤ(3) parafermionic chain emerging from Yang-Baxter equation Yu, Li-Wei Ge, Mo-Lin Sci Rep Article We construct the 1D [Image: see text] parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the [Image: see text] parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the [Image: see text] parafermionic model is a direct generalization of 1D [Image: see text] Kitaev model. Both the [Image: see text] and [Image: see text] model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian [Image: see text] based on Yang-Baxter equation. Different from the Majorana doubling, the [Image: see text] holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P[Image: see text] and emergent parafermionic operator Γ, which are the generalizations of parity P(M) and emergent Majorana operator in Lee-Wilczek model, respectively. Both the [Image: see text] parafermionic model and [Image: see text] can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation. Nature Publishing Group 2016-02-23 /pmc/articles/PMC4794089/ /pubmed/26902999 http://dx.doi.org/10.1038/srep21497 Text en Copyright © 2016, Macmillan Publishers Limited 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
Yu, Li-Wei
Ge, Mo-Lin
ℤ(3) parafermionic chain emerging from Yang-Baxter equation
title ℤ(3) parafermionic chain emerging from Yang-Baxter equation
title_full ℤ(3) parafermionic chain emerging from Yang-Baxter equation
title_fullStr ℤ(3) parafermionic chain emerging from Yang-Baxter equation
title_full_unstemmed ℤ(3) parafermionic chain emerging from Yang-Baxter equation
title_short ℤ(3) parafermionic chain emerging from Yang-Baxter equation
title_sort ℤ(3) parafermionic chain emerging from yang-baxter equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4794089/
https://www.ncbi.nlm.nih.gov/pubmed/26902999
http://dx.doi.org/10.1038/srep21497
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