A supervised learning algorithm for interacting topological insulators based on local curvature

TL;DR

This paper introduces a supervised machine learning approach that uses local curvature data at high symmetry points to efficiently identify topological phases in interacting topological insulators across various dimensions and symmetry classes.

Contribution

The study presents a novel neural network method that predicts topological phases from local curvature data, revealing interaction-induced topological multicriticality.

Findings

Neural network accurately predicts topological phases in interacting systems.

Method uncovers interaction-induced topological multicriticality.

Efficient identification of topological phases with minimal data.

Abstract

Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We apply this scheme to a variety of interacting topological insulators in different dimensions and symmetry classes, and demonstrate that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases with very little numerical effort. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality in the examples studied.