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

Journal Article · Tue Jul 15 00:00:00 EDT 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.10.002· OSTI ID:21163717

Hikami, Kazuhiro ^[1]

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1. Department of Physics, Graduate School of Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033 (Japan)

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.

• OSTI ID: 21163717
• Journal Information: Annals of Physics (New York), Vol. 323, 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); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
HALL EFFECT
MATRICES
QUANTUM ENTANGLEMENT
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUASI PARTICLES
SPIN
TOPOLOGY