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

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.

8 pages, 3 figures - corrected typos in Fig. 1

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Cited by in corpus (8)

• Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Experimental demonstration of adversarial examples in learning topological phases
• Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Learning phases with Quantum Monte Carlo simulation cell
• Classifying topological neural network quantum states via diffusion maps
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions