Title: Interface contributions to topological entanglement in abelian Chern-Simons theory

Abstract

Here, we study the entanglement entropy between (possibly distinct) topological phases across an interface using an Abelian Chern-Simons description with topological boundary conditions (TBCs) at the interface. From a microscopic point of view, these TBCs correspond to turning on particular gapping interactions between the edge modes across the interface. However, in studying entanglement in the continuum Chern-Simons description, we must confront the problem of non-factorization of the Hilbert space, which is a standard property of gauge theories. We carefully define the entanglement entropy by using an extended Hilbert space construction directly in the continuum theory. We show how a given TBC isolates a corresponding gauge invariant state in the extended Hilbert space, and hence compute the resulting entanglement entropy. We find that the sub-leading correction to the area law remains universal, but depends on the choice of topological boundary conditions. This agrees with the microscopic calculation of [1]. Additionally, we provide a replica path integral calculation for the entropy. In the case when the topological phases across the interface are taken to be identical, our construction gives a novel explanation of the equivalence between the left-right entanglement of (1+1)d Ishibashi states and the spatial entanglement of (2+1)d topological phases.

Authors:

Fliss, Jackson R. ^[1]; Wen, Xueda ^[2]; Parrikar, Onkar ^[3]; Hsieh, Chang -Tse ^[1]; Han, Bo ^[1]; Hughes, Taylor L. ^[1]; Leigh, Robert G. ^[1]

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+ Show Author Affiliations

1. Univ. of Illinois, Urbana, IL (United States)
2. Univ. of Illinois, Urbana, IL (United States); Univ. of California, Santa Barbara, CA (United States)
3. Univ. of Pennsylvania, Philadelphia, PA (United States)

Publication Date:

2017-09-14

Research Org.:

Univ. of Illinois, Urbana (United States)

Sponsoring Org.:

USDOE

OSTI Identifier:

1465511

Grant/Contract Number:  

FG02-13ER42001; SC0009932

Resource Type:

Accepted Manuscript

Journal Name:

Journal of High Energy Physics (Online)

Additional Journal Information:

Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:

Springer Berlin

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons Theories; Topological Field Theories; Gauge Symmetry; Topological States of Matter