SciPost Physics

SciPost Phys. 11, 073 (2021) · published 28 September 2021

• doi: 10.21468/SciPostPhys.11.3.073
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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. We 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.

• Uría-Álvarez et al., Deep learning for disordered topological insulators through their entanglement spectrum
  Phys. Rev. B 105, 155128 (2022) [Crossref]
• Chen et al., Measurement of interaction-dressed Berry curvature and quantum metric in solids by optical absorption
  SciPost Phys. Core 5, 040 (2022) [Crossref]
• Molignini et al., Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
  SciPost Phys. Core 6, 059 (2023) [Crossref]
• Yu et al., Unsupervised learning of interacting topological phases from experimental observables
  Fundamental Research 4, 1086 (2024) [Crossref]
• Du et al., Higher-order topological insulators by ML-enhanced topology optimization
  International Journal of Mechanical Sciences 255, 108441 108441 (2023) [Crossref]
• Tibaldi et al., Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions
  SciPost Phys. 14, 005 (2023) [Crossref]
• Zhang et al., Experimental demonstration of adversarial examples in learning topological phases
  Nat Commun 13, 4993 (2022) [Crossref]
• Teng et al., Clustering neural quantum states via diffusion maps
  Phys. Rev. B 108, 205152 (2023) [Crossref]
• Ghosh et al., Supervised learning of an interacting two-dimensional hardcore boson model of a weak topological insulator using correlation functions
  Phys. Rev. B 110, 165134 (2024) [Crossref]