Non-Abelian statistics of vortices with multiple Majorana fermions

Yuji Hirono, Shigehiro Yasui, Kazunori Itakura, Muneto Nitta

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We consider the exchange statistics of vortices, each of which traps an odd number (N) of Majorana fermions. We assume that the fermions in a vortex transform in the vector representation of the SO(N) group. Exchange of two vortices turns out to be non-Abelian, and the corresponding operator is further decomposed into two parts: a part that is essentially equivalent to the exchange operator of vortices having a single Majorana fermion in each vortex, and a part representing the Coxeter group. Similar decomposition was already found in the case with N=3, and the result shown here is a generalization to the case with an arbitrary odd N. We can obtain the matrix representation of the exchange operators in the Hilbert space that is constructed by using Dirac fermions nonlocally defined by Majorana fermions trapped in separated vortices. We also show that the decomposition of the exchange operator implies tensor-product structure in its matrix representation.

Original languageEnglish
Article number014508
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume86
Issue number1
DOIs
Publication statusPublished - 2012 Jul 10

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Fermions
Vortex flow
fermions
Statistics
statistics
vortices
operators
Decomposition
decomposition
Hilbert spaces
matrices
Hilbert space
Tensors
Mathematical operators
Ion exchange
traps
tensors
products

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

Non-Abelian statistics of vortices with multiple Majorana fermions. / Hirono, Yuji; Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 86, No. 1, 014508, 10.07.2012.

Research output: Contribution to journalArticle

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