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Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids

Shiying Dong1, Eduardo Fradkin1, Robert G. Leigh1 and Sean Nowling1,2

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We compute directly the entanglement entropy of spatial regions in Chern-Simons gauge theories in 2+1 dimensions using surgery. We consider the possible dependence of the entanglement entropy on the topology of the spatial manifold and on the vacuum state on that manifold. The entanglement entropy of puncture insertions (quasiparticles) is discussed in detail for a few cases of interest. We show that quite generally the topological entanglement entropy is determined by the modular Script S-matrix of the associated rational conformal field theory as well as by the fusion rules and fusion coefficients. We use these results to determine the universal topological piece of the entanglement entropy for Abelian and non-Abelian quantum Hall fluids. As a byproduct we present the calculation of the modular Script S-matrix of two coset RCFTs of interest.

Keywords

Topological Field Theories

Chern-Simons Theories

PACS

11.15.-q Gauge field theories

02.40.-k Geometry, differential geometry, and topology

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

11.25.Hf Conformal field theory, algebraic structures

Subjects

Mathematical physics

Quantum information and quantum mechanics

Particle physics and field theory

Dates

Issue 05 (May 2008)

Received 9 April 2008, accepted for publication 15 April 2008

Published 7 May 2008



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