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.

arXiv comment8 pages, 3 figures - corrected typos in Fig. 1

References in corpus (51)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Single particle Green's functions and interacting topological insulators
• Machine Learning Topological States
• Identifying topological order through unsupervised machine learning
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Unsupervised machine learning and band topology
• Electron-phonon Coupling on the Surface of the Topological Insulator Bi2Se3: Determined from Surface Phonon Dispersion Measurements
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Distinguishing bulk and surface electron-phonon coupling in the topological insulator Bi2Se3 using time-resolved photoemission spectroscopy
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Two-dimensional universal conductance fluctuations and the electron-phonon interaction of topological surface states in Bi2Te2Se nanoribbons
• Intrinsic Electron-Phonon Resistivity in Bi2Se3 in the Topological Regime
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• Deep Learning Topological Invariants of Band Insulators
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Unsupervised identification of topological order using predictive models
• Universality classes of topological phase transitions with higher-order band crossing
• Many-body effects and possible superconductivity in the 2D metallic surface states of 3D topological insulators
• Electron-Phonon Coupling and Surface Debye Temperature of Bi${}_2$Te${}_3$(111) from Helium Atom Scattering
• Multi-critical Behavior in Topological Phase Transitions
• Machine learning topological phases in real space
• Optical phonon dynamics and electronic fluctuations in the Dirac semimetal Cd3As2
• Scaling Theory of Topological Phase Transitions
• Acoustic phonon dynamics in thin-films of the topological insulator Bi2Se3
• Electron-phonon interaction on the surface of a 3D topological insulator
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Generating quantum multi-criticality in topological insulators by periodic driving
• Fidelity susceptibility near topological phase transitions in quantum walks
• Scaling Theory of ${\mathbb{Z}}_2$ Topological Invariants
• Plasmon-enhanced electron-phonon coupling in Dirac surface states of the thin-film topological insulator Bi2Se3
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Unification of topological invariants in Dirac models
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Multi-critical topological transition at quantum criticality
• Phonon structure in dispersion curves and density of states of massive Dirac Fermions
• Connecting electron and phonon spectroscopy data to consistently determine quasiparticle-phonon coupling on the surface of topological insulators
• Edge mode manipulation through commensurate multifrequency driving
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Multicriticality in a one-dimensional topological band insulator
• Curvature function renormalisation, topological phase transitions and multicriticality
• Renormalization group approach to symmetry protected topological phases
• Scaling behavior in a multicritical one-dimensional topological insulator
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators

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