Interface contributions to topological entanglement in abelian Chern-Simons theory
- Univ. of Illinois, Urbana, IL (United States)
- Univ. of Illinois, Urbana, IL (United States); Univ. of California, Santa Barbara, CA (United States)
- Univ. of Pennsylvania, Philadelphia, PA (United States)
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.
- Research Organization:
- Univ. of Illinois, Urbana (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- FG02-13ER42001; SC0009932
- OSTI ID:
- 1465511
- Journal Information:
- Journal of High Energy Physics (Online), Vol. 2017, Issue 9; ISSN 1029-8479
- Publisher:
- Springer BerlinCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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