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Topological Entanglement Entropy from the Holographic Partition Function

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Abstract

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.

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Authors and Affiliations

  1. Department of Physics, University of Virginia, Charlottesville, VA, 22904-4714, USA

    Paul Fendley

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, USA

    Matthew P. A. Fisher

  3. Microsoft Project Q, University of California, Santa Barbara, CA, 93106-4030, USA

    Chetan Nayak

  4. Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095-1547, USA

    Chetan Nayak

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  1. Paul Fendley
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  2. Matthew P. A. Fisher
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  3. Chetan Nayak
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Fendley, P., Fisher, M.P.A. & Nayak, C. Topological Entanglement Entropy from the Holographic Partition Function. J Stat Phys 126, 1111–1144 (2007). https://doi.org/10.1007/s10955-006-9275-8

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  • DOI: https://doi.org/10.1007/s10955-006-9275-8

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