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Title: Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

Abstract

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2){sub K} Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.

Authors:
 [1]
  1. Department of Physics, Graduate School of Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033 (Japan)
Publication Date:
OSTI Identifier:
21163717
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 323; Journal Issue: 7; Other Information: DOI: 10.1016/j.aop.2007.10.002; PII: S0003-4916(07)00152-2; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; HALL EFFECT; MATRICES; QUANTUM ENTANGLEMENT; QUANTUM FIELD THEORY; QUANTUM MECHANICS; QUASI PARTICLES; SPIN; TOPOLOGY

Citation Formats

Hikami, Kazuhiro. Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states. United States: N. p., 2008. Web. doi:10.1016/j.aop.2007.10.002.
Hikami, Kazuhiro. Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states. United States. https://doi.org/10.1016/j.aop.2007.10.002
Hikami, Kazuhiro. 2008. "Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states". United States. https://doi.org/10.1016/j.aop.2007.10.002.
@article{osti_21163717,
title = {Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states},
author = {Hikami, Kazuhiro},
abstractNote = {We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2){sub K} Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.},
doi = {10.1016/j.aop.2007.10.002},
url = {https://www.osti.gov/biblio/21163717}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 7,
volume = 323,
place = {United States},
year = {Tue Jul 15 00:00:00 EDT 2008},
month = {Tue Jul 15 00:00:00 EDT 2008}
}