Detecting topological order in a ground state wave function

TL;DR

This paper introduces a method to detect topological order in ground state wave functions by computing the topological entropy, which measures the quantum dimension related to string-net condensation.

Contribution

It provides a novel approach to identify topological order directly from the ground state wave function using topological entropy.

Findings

Topological entropy can be computed from ground state wave functions.

The method effectively measures the quantum dimension D.

Applicable to a broad class of topological orders.

Abstract

A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d_i, F^{ijk}_{lmn}, \delta_{ijk}). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the ``topological entropy'' which directly measures the quantum dimension D = \sum_i d^2_i.