Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions

Abstract

Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and diffusive metal. As in the previous paper on two-dimensional quantum phase transitions [J. Phys. Soc. Jpn. vol. 85, 123706 (2016)], we use an image recognition algorithm based on a multilayered convolutional neural network to identify which phase the eigenfunction belongs to. The Anderson model for localization-delocalization transition, the Wilson--Dirac model for topological insulators, and the layered Chern insulator model for Weyl semimetal are studied. The situation where the standard transfer matrix approach is not applicable is also treated by this method.

16 pages, 6 figures. Text and references revised. Open access

References in corpus (15)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Scheme to Achieve Silicon Topological Photonics
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological Anderson Insulator
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Topological Anderson Insulator in Three Dimensions
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Pure density functional for strong correlations and the thermodynamic limit from machine learning
• Observation of the quantum-anomalous-Hall insulator to Anderson insulator quantum phase transition and its scaling behavior
• Single-particle excitations under coexisting electron correlation and disorder: a numerical study of the Anderson-Hubbard model
• Finite-size energy gap in weak and strong topological insulators
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality

Cited by in corpus (3)

• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network