Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators

Quantum material phases such as Anderson insulator, diffusive metal, 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 are 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 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 derives topological phase transition. The results are confirmed by independent calculations of localization length, density of states, and wave packet dynamics.

Reference:
T. Mano and T. Ohtsuki: arxiv:1910.03194, to appear in J. Phys. Soc. Jpn.