Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators

Abstract

Quantum material phases such as the Anderson insulator, diffusive metal, and Weyl/Dirac semimetal as well as topological insulators show specific wave functions both in real and Fourier spaces. These features are well captured by convolutional neural networks, and the phase diagrams have been obtained, where standard methods are not applicable. One of these examples is the cases of random lattices such as quantum percolation. Here, we study the topological insulators with random vacancies, namely, the quantum percolation in topological insulators, by analyzing the wave functions via a convolutional neural network. The vacancies in topological insulators are especially interesting since peculiar bound states are formed around the vacancies. We show that only a few percent of vacancies are required for a topological phase transition. The results are confirmed by independent calculations of localization length, density of states, and wave packet dynamics.

arXiv commentpublished version. Open access

References in corpus (41)

• Topological Insulators
• Topological insulators and superconductors
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological Insulator Materials
• Machine learning phases of matter
• The Kernel Polynomial Method
• Model Hamiltonian for Topological Insulators
• Learning phase transitions by confusion
• Topological Anderson Insulator
• Riemannian symmetric superspaces and their origin in random matrix theory
• Theory of the topological Anderson insulator
• A Density Matrix-based Algorithm for Solving Eigenvalue Problems
• Machine learning quantum phases of matter beyond the fermion sign problem
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Topological Insulators in Random Lattices
• Topological Anderson Insulator in Three Dimensions
• Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
• Bond and Site Percolation in Three Dimensions
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Disordered weak and strong topological insulators
• Anomalous diffusion at the Anderson transitions
• Unconventional localisation transition in high dimensions
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• Learning Disordered Topological Phases by Statistical Recovery of Symmetry
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Real space mapping of topological invariants using artificial neural networks
• Z2 invariant protected bound states in topological insulators
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Finite-size energy gap in weak and strong topological insulators
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Three-Dimensional Quantum Percolation Studied by Level Statistics
• Dimensional crossover of transport characteristics in topological insulator nanofilms
• Comparative numerical study of Anderson localization in disordered electron systems
• Elastic Anomaly of Helium Films at a Quantum Phase Transition
• Protection of the surface states in topological insulators: Berry phase perspective

Cited by in corpus (12)

• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Amorphous topological matter: theory and experiment
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Unsupervised learning using topological data augmentation
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Topological Random Fractals
• Topological diffusive metal in amorphous transition metal monosilicides
• Ballistic transport in disordered Dirac and Weyl semimetals
• Machine learning the dynamics of quantum kicked rotor
• Quaternion-based machine learning on topological quantum systems
• Analysis of Kohn-Sham Eigenfunctions Using a Convolutional Neural Network in Simulations of the Metal-insulator Transition in Doped Semiconductors
• Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness