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Title: Anyonic entanglement and topological entanglement entropy

Abstract

We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy. - Highlights: • Entanglement of anyonic systems is studied using standard notions of entropy. • The algebraic theory of anyon models for higher genus surfaces is developed. • A general method for calculating topological entanglement entropy is presented. • Topological entanglement entropy originates from conservation of topological charge.

Authors:
 [1];  [2];  [2]
  1. Station Q, Microsoft Research, Santa Barbara, CA 93106-6105 (United States)
  2. Department of Physics, University of California, Santa Barbara, CA 93106 (United States)
Publication Date:
OSTI Identifier:
22701541
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 385; Other Information: Copyright (c) 2017 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; ANYONS; ENTROPY; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Bonderson, Parsa, Knapp, Christina, and Patel, Kaushal. Anyonic entanglement and topological entanglement entropy. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.07.018.
Bonderson, Parsa, Knapp, Christina, & Patel, Kaushal. Anyonic entanglement and topological entanglement entropy. United States. https://doi.org/10.1016/J.AOP.2017.07.018
Bonderson, Parsa, Knapp, Christina, and Patel, Kaushal. 2017. "Anyonic entanglement and topological entanglement entropy". United States. https://doi.org/10.1016/J.AOP.2017.07.018.
@article{osti_22701541,
title = {Anyonic entanglement and topological entanglement entropy},
author = {Bonderson, Parsa and Knapp, Christina and Patel, Kaushal},
abstractNote = {We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy. - Highlights: • Entanglement of anyonic systems is studied using standard notions of entropy. • The algebraic theory of anyon models for higher genus surfaces is developed. • A general method for calculating topological entanglement entropy is presented. • Topological entanglement entropy originates from conservation of topological charge.},
doi = {10.1016/J.AOP.2017.07.018},
url = {https://www.osti.gov/biblio/22701541}, journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 385,
place = {United States},
year = {Sun Oct 15 00:00:00 EDT 2017},
month = {Sun Oct 15 00:00:00 EDT 2017}
}