Error-correction properties of an interacting topological insulator

TL;DR

This paper investigates the phase diagram of an interacting topological insulator model with antiferromagnetic interactions, using a novel error correction-based approach to identify topological phases and their transitions.

Contribution

It introduces an operational error correction framework to analyze topological order in an interacting insulator model, revealing distinct topological phases and phase transitions.

Findings

Identified two symmetry-protected topological phases.

Developed an efficient Monte Carlo sampling method for error correction statistics.

Classified thermodynamic phases using error correction, including a trivial antiferromagnetic phase.

Abstract

We analyze the phase diagram of a topological insulator model including antiferromagnetic interactions in the form of an extended Su-Schrieffer Heeger model. To this end, we employ a recently introduced operational definition of topological order based on the ability of a system to perform topological error correction. We show that the necessary error correction statistics can be obtained efficiently using a Monte-Carlo sampling of a matrix product state representation of the ground state wave function. Specifically, we identify two distinct symmetry-protected topological phases corresponding to two different fully dimerized reference states. Finally, we extend the notion of error correction to classify thermodynamic phases to those exhibiting local order parameters, finding a topologically trivial antiferromagnetic phase for sufficiently strong interactions.