TY - JOUR

T1 - Interface contributions to topological entanglement in abelian Chern-Simons theory

AU - Fliss, Jackson R.

AU - Wen, Xueda

AU - Parrikar, Onkar

AU - Hsieh, Chang Tse

AU - Han, Bo

AU - Hughes, Taylor L.

AU - Leigh, Robert G.

N1 - Funding Information:
We would like to acknowledge helpful conversations with Vijay Balasubramanian, Jennifer Cano, Aitor Lewkowyzc, Michael Mulligan, Charles Rabideau, and Luiz Santos. OP wishes to acknowledge support from the Simons foundation (# 385592, Vijay Balasubramanian) through the It from Qubit collaboration. TLH acknowledges the support of National Science Foundation CAREER Grant No. DMR-1351895 and the ICMT at UIUC. RGL is supported by the US Department of Energy under contract DE-FG02-13ER42001.
Publisher Copyright:
© 2017, The Author(s).

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Chern-Simons Theories

KW - Gauge Symmetry

KW - Topological Field Theories

KW - Topological States of Matter

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U2 - 10.1007/JHEP09(2017)056

DO - 10.1007/JHEP09(2017)056

M3 - Article

AN - SCOPUS:85029750756

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 56

ER -