Determining topological order from infinite projected entangled pair states

TL;DR

This paper introduces a method to extract topological order information from 2D strongly correlated systems' ground states using iPEPS, accurately computing topological invariants even near phase transitions.

Contribution

The authors develop a robust algorithm utilizing iPEPS and iMPO to determine topological data, including S and T matrices, from ground states, effective near quantum phase transitions.

Findings

Successfully computes topological S and T matrices from iPEPS.

Robust against phase transitions with large correlation lengths.

Achieves excellent agreement with theoretical predictions for the Kitaev model.

Abstract

We present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators (iMPO) onto states with well-defined anyon flux are used to compute topological $S$ and $T$ matrices (encoding mutual- and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.