Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network

TL;DR

This paper employs deep 3D convolutional neural networks to analyze phase transitions in 3D Anderson and quantum percolation models, enabling comprehensive phase diagram mapping from wave function data.

Contribution

It introduces the use of 3D CNNs for full phase diagram determination in 3D disordered systems, extending previous 2D recognition methods.

Findings

Full phase diagrams obtained using 3D CNN trained at band center.

Phase diagrams for quantum bond and site percolation derived from Anderson model training.

Demonstrated effectiveness of 3D image recognition in analyzing 3D quantum phase transitions.

Abstract

The three-dimensional Anderson model is a well-studied model of disordered electron systems that shows the delocalization--localization transition. As in our previous papers on two- and three-dimensional (2D, 3D) quantum phase transitions [J. Phys. Soc. Jpn. {\bf 85}, 123706 (2016), {\bf 86}, 044708 (2017)], we used an image recognition algorithm based on a multilayered convolutional neural network. However, in contrast to previous papers in which 2D image recognition was used, we applied 3D image recognition to analyze entire 3D wave functions. We show that a full phase diagram of the disorder-energy plane is obtained once the 3D convolutional neural network has been trained at the band center. We further demonstrate that the full phase diagram for 3D quantum bond and site percolations can be drawn by training the 3D Anderson model at the band center.