Abstract
Paul Fendley (University of Virginia, Charlottesville / Oxford)
Topological Entanglement Entropy from the Holographic Partition Function
I explain how the entanglement entropy of both the gapped bulk excitations and the gapless edge modes in a 2+1 dimensional topological phase 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. Examples include abelian and non-abelian fractional quantum Hall states, and p+ip superconductors. Including a point contact allows tunneling between two points on the edge, causing thermodynamic entropy to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and the thermodynamic entropy loss is the same as that of the edge entanglement entropy. The non-integer `ground state degeneracy' obtained in 1+1-dimensional quantum impurity problems then has a nice interpretation: its logarithm is a 2+1-dimensional topological entanglement entropy.