Detecting Topological Order in a Ground State Wave Function

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 $(N,d_i,F_{lmn}^{ijk},{\delta }_{ijk})$. 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 total quantum dimension $D=\sum _i{d}_i^2$.