Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions

Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and diffusive metal. As in the previous paper on two-dimensional quantum phase transitions [J. Phys. Soc. Jpn. 85, 123706 (2016)], we use an image recognition algorithm based on a multilayered convolutional neural network to identify which phase the eigenfunction belongs to. The Anderson model for localization-delocalization transition, the Wilson-Dirac model for topological insulators, and the layered Chern insulator model for Weyl semimetal are studied. The situation where the standard transfer matrix approach is not applicable is also treated by this method.