Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions

TL;DR

This paper demonstrates how deep learning neural networks can analyze wave functions to accurately map phase diagrams of various disordered quantum systems, offering a new approach to identifying quantum phases.

Contribution

It introduces a neural network-based method for determining quantum phases from wave functions, enabling phase diagram construction in complex disordered systems.

Findings

Successfully mapped phase diagrams of Anderson transitions and topological systems

Validated the method on 2D and 3D disordered quantum systems

Compared advantages and disadvantages with traditional techniques

Abstract

Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. Obtaining and representing the ground and excited state wave functions are examples of such applications. Another application is analyzing the wave functions and determining their quantum phases. Here, we review the recent progress of using the multilayer convolutional neural network, so-called deep learning, to determine the quantum phases in random electron systems. After training the neural network by the supervised learning of wave functions in restricted parameter regions in known phases, the neural networks can determine the phases of the wave functions in wide parameter regions in unknown phases; hence, the phase diagrams are obtained. We demonstrate the validity and generality of this method by drawing the phase diagrams of two- and higher dimensional Anderson metal-insulator transitions and quantum percolations as well as disordered topological systems such as three-dimensional topological insulators and Weyl semimetals. Both real-space and Fourier space wave functions are analyzed. The advantages and disadvantages over conventional methods are discussed.