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

• URL: http://arxiv.org/abs/2104.11237v2
• Date: Wed, 5 May 2021 18:32:35 GMT
• Title: A supervised learning algorithm for interacting topological insulators based on local curvature
• Authors: Paolo Molignini, Antonio Zegarra, Evert van Nieuwenburg, R. Chitra, and Wei Chen
• Abstract summary: We introduce a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We show that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality.
• Score: 6.281776745576886
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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