Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators

TL;DR

This paper demonstrates how convolutional neural networks can effectively analyze quantum phase transitions in topological insulators with random vacancies, revealing that a small vacancy concentration can induce a topological phase change.

Contribution

It introduces a CNN-based approach to study quantum percolation in topological insulators, capturing phase transitions not accessible by standard methods.

Findings

Few percent vacancies cause topological phase transition.

CNN accurately identifies phase boundaries.

Results confirmed by localization length and wave dynamics.

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.