Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics

Shigehiro Yasui, Kazunori Itakura, Muneto Nitta

研究成果: Article

17 引用 (Scopus)

抄録

We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.

元の言語English
記事番号134518
ジャーナルPhysical Review B - Condensed Matter and Materials Physics
83
発行部数13
DOI
出版物ステータスPublished - 2011 4 25

Fingerprint

Fermions
fermions
Statistics
statistics
Vortex flow
vortices
polytopes
Hilbert spaces
Hilbert space
Tensors
tensors
symmetry
products

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

これを引用

Majorana meets Coxeter : Non-Abelian Majorana fermions and non-Abelian statistics. / Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto.

:: Physical Review B - Condensed Matter and Materials Physics, 巻 83, 番号 13, 134518, 25.04.2011.

研究成果: Article

@article{7ded111be7604e7d89e43e70edbcbade,
title = "Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics",
abstract = "We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.",
author = "Shigehiro Yasui and Kazunori Itakura and Muneto Nitta",
year = "2011",
month = "4",
day = "25",
doi = "10.1103/PhysRevB.83.134518",
language = "English",
volume = "83",
journal = "Physical Review B-Condensed Matter",
issn = "1098-0121",
publisher = "American Physical Society",
number = "13",

}

TY - JOUR

T1 - Majorana meets Coxeter

T2 - Non-Abelian Majorana fermions and non-Abelian statistics

AU - Yasui, Shigehiro

AU - Itakura, Kazunori

AU - Nitta, Muneto

PY - 2011/4/25

Y1 - 2011/4/25

N2 - We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.

AB - We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.

UR - http://www.scopus.com/inward/record.url?scp=79961073141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961073141&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.83.134518

DO - 10.1103/PhysRevB.83.134518

M3 - Article

AN - SCOPUS:79961073141

VL - 83

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 13

M1 - 134518

ER -