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:
-
- 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}
}
Other availability
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.