Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems

Abstract

Random electron systems show rich phases such as Anderson insulator, diffusive metal, quantum and anomalous quantum Hall insulator, Weyl semimetal, as well as strong/weak topological insulators. Eigenfunctions of each matter phase have specific features, but due to the random nature of systems, judging the matter phase from eigenfunctions is difficult. Here we propose the deep learning algorithm to capture the features of eigenfunctions. Localization-delocalization transition as well as disordered Chern insulator-Anderson insulator transition is discussed.

14 pages including Supplemental material. Published version

References in corpus (6)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Observation of the quantum-anomalous-Hall insulator to Anderson insulator quantum phase transition and its scaling behavior
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality

Cited by in corpus (38)

• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Solving the Bose-Hubbard model with machine learning
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Machine learning dynamical phase transitions in complex networks
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Few-shot machine learning in the three-dimensional Ising model
• Machine learning of phase transitions in nonlinear polariton lattices
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Distinguishing an Anderson Insulator from a Many-Body Localized phase through space-time snapshots with Neural Networks
• Learning epidemic threshold in complex networks by Convolutional Neural Network
• Can a CNN trained on the Ising model detect the phase transition of the $q$-state Potts model?
• Machine Learning Phase Diagram in the Half-filled One-dimensional Extended Hubbard Model
• Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Machine Learning the Square-Lattice Ising Model
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Machine learning of phases and structures for model systems in physics
• Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects
• Efficient and quantum-adaptive machine learning with fermion neural networks
• Machine learning phases of an Abelian gauge theory
• Neural Network Approach to Scaling Analysis of Critical Phenomena
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Learning What a Machine Learns in a Many-Body Localization Transition
• Probing transport in quantum many-fermion simulations via quantum loop topography
• Noise signal as input data in self-organized neural networks
• Learning phases with Quantum Monte Carlo simulation cell
• Phase classification in the long-range Harper model using machine learning
• Renormalization-group-inspired neural networks for computing topological invariants
• Many-body mobility edges in 1D and 2D revealed by convolutional neural networks
• Comments on the minimal training set for CNN: a case study of the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Neural Scaling Laws for Deep Regression
• Numerical methods for localization
• Deep learning of topological phase transitions from entanglement aspects: An unsupervised way
• Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness
• Deep learning of thermodynamic laws from microscopic dynamics