Entanglement interferometry and anyons

Excitations with anyon statistics can emerge from a system of ordinary bosons or fermions, in special phases such as the fractional quantum Hall states. They have quantized properties that do not change when interaction potentials are tuned, indicating that they are related to some underlying order parameter (known as topological order) the way dislocations in a crystal are characteristic of the particular crystalline structure. Thus it should be possible to determine the statistics of the anyonic excitations without actually creating them, just from the ground state wave function.

I will present a method for determining the anyonic statistics of a topological state using the degenerate ground state wave functions on a torus. The idea is to study interference oscillations in the entanglement entropy as a function of the ground state as a way to identify ground states that correspond to anyons, and to determine the statistics (more precisely the S-matrix) from them.