General procedure for determining braiding and statistics of anyons using entanglement interferometry

TL;DR

This paper introduces a symmetry-free entanglement interferometry method to determine the braiding statistics of anyons in topological phases by analyzing MESs from three bipartitions of the torus.

Contribution

It presents a novel procedure to extract the modular S matrix without relying on lattice symmetries or quasiparticle labeling assumptions.

Findings

Successfully determines the modular S matrix for various topological phases.

Provides strong constraints on the T and U matrices without symmetry assumptions.

Applicable to both Abelian and non-Abelian topological phases.

Abstract

Recently, it was argued that the braiding and statistics of anyons in a two-dimensional topological phase can be extracted by studying the quantum entanglement of the degenerate ground-states on the torus. This construction either required a lattice symmetry (such as $\pi/2$ rotation) or tacitly assumed that the `minimum entanglement states' (MESs) for two different bipartitions can be uniquely assigned quasiparticle labels. Here we describe a procedure to obtain the modular $\mathcal S$ matrix, which encodes the braiding statistics of anyons, which does not require making any of these assumptions. Our strategy is to compare MESs of three independent entanglement bipartitions of the torus, which leads to a unique modular $\mathcal S$. This procedure also puts strong constraints on the modular $\mathcal T$ and $\mathcal U$ matrices without requiring any symmetries, and in certain special cases, completely determines it. Our method applies equally to Abelian and non-Abelian topological phases.