Topological Entanglement Entropy from the Holographic Partition Function

TL;DR

This paper develops a holographic approach to compute the entanglement entropy in 2+1-dimensional topological phases, linking bulk and edge excitations through a conformal field theory partition function.

Contribution

It introduces a general holographic partition function framework for topological phases, connecting edge CFTs with bulk entanglement entropy, including effects of point contacts and tunneling.

Findings

Holographic partition function encodes bulk and edge entanglement entropy.

Edge tunneling reduces thermodynamic entropy, reflecting entanglement loss.

Topological entanglement entropy relates to ground state degeneracy in impurity problems.

Abstract

We study the entropy of chiral 2+1-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.