Anyonic entanglement and topological entanglement entropy
- Station Q, Microsoft Research, Santa Barbara, CA 93106-6105 (United States)
- Department of Physics, University of California, Santa Barbara, CA 93106 (United States)
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.
- OSTI ID:
- 22701541
- Journal Information:
- Annals of Physics, Vol. 385; Other Information: Copyright (c) 2017 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
Similar Records
Prediction of Toric Code Topological Order from Rydberg Blockade
Bosons, fermions and anyons in the plane, and supersymmetry