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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:
 [1];  [2];  [3];  [1];  [1];  [1];  [1]
  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:
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

Citation Formats

Fliss, Jackson R., Wen, Xueda, Parrikar, Onkar, Hsieh, Chang -Tse, Han, Bo, Hughes, Taylor L., and Leigh, Robert G. Interface contributions to topological entanglement in abelian Chern-Simons theory. United States: N. p., 2017. Web. doi:10.1007/JHEP09(2017)056.
Fliss, Jackson R., Wen, Xueda, Parrikar, Onkar, Hsieh, Chang -Tse, Han, Bo, Hughes, Taylor L., & Leigh, Robert G. Interface contributions to topological entanglement in abelian Chern-Simons theory. United States. doi:10.1007/JHEP09(2017)056.
Fliss, Jackson R., Wen, Xueda, Parrikar, Onkar, Hsieh, Chang -Tse, Han, Bo, Hughes, Taylor L., and Leigh, Robert G. Thu . "Interface contributions to topological entanglement in abelian Chern-Simons theory". United States. doi:10.1007/JHEP09(2017)056. https://www.osti.gov/servlets/purl/1465511.
@article{osti_1465511,
title = {Interface contributions to topological entanglement in abelian Chern-Simons theory},
author = {Fliss, Jackson R. and Wen, Xueda and Parrikar, Onkar and Hsieh, Chang -Tse and Han, Bo and Hughes, Taylor L. and Leigh, Robert G.},
abstractNote = {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.},
doi = {10.1007/JHEP09(2017)056},
journal = {Journal of High Energy Physics (Online)},
number = [9],
volume = [2017],
place = {United States},
year = {2017},
month = {9}
}

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Cited by: 12 works
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