Determining non-Abelian topological order from infinite projected entangled pair states

TL;DR

This paper extends a method to identify non-Abelian topological order in two-dimensional quantum systems using infinite projected entangled pair states, enabling the calculation of topological invariants and anyon statistics.

Contribution

It introduces a new approach to extract non-Abelian topological order from iPEPS by analyzing symmetries and fusion rules, and computes topological invariants efficiently.

Findings

Successfully applied to Fibonacci and Ising string net models.

Able to determine topological S and T matrices from ground states.

Provides a practical algorithm for identifying non-Abelian topological phases.

Abstract

We generalize the method introduced in Phys. Rev. B 101, 041108 (2020) of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state (iPEPS) to non-Abelian topological order. When wrapped on a torus the unique iPEPS becomes a superposition of degenerate and locally indistinguishable ground states. We find numerically symmetries of the iPEPS, represented by infinite matrix product operators (MPO), and their fusion rules. The rules tell us how to combine the symmetries into projectors onto states with well defined anyon flux. A linear structure of the MPO projectors allows for efficient determination for each state its second Renyi topological entanglement entropy on an infinitely long cylinder directly in the limit of infinite cylinder's width. The same projectors are used to compute topological $S$ and $T$ matrices encoding mutual- and self-statistics of emergent anyons. The algorithm is illustrated by examples of Fibonacci and Ising non-Abelian string net models.