Mathematical and Theoretical Physics Seminar: "Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory"
(sign-up)Jackson Fliss, University of Illinois at Urbana Champaign
Physics and Mathematics
In this talk I will discuss the entanglement entropy between two (possibly) distinct topological phases in Abelian Chern-Simons theory. At the interface between the phases, two issues must be addressed: (i) what are the boundary conditions that correspond to the interface being gapped?, and (ii) how does one define entanglement in continuum gauge theories where the Hilbert space typically does not admit a tensor product factorization? For the former question it is known that gapped interfaces are described by a class of boundary conditions known as topological boundary conditions (TBCs). I will describe how TBCs also address the latter question by isolating a unique gauge invariant state in the extended Hilbert space approach. I will show that upon computing the entanglement entropy, the universal correction to the area law retains a dependence on the choice of TBCs. This result matches previous microscopic calculations found in the condensed matter literature. Additionally, when the phases across the interface are taken to be identical, this construction provides 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.
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