Applications of multilayer convolutional neural network to quantum phase transitions in disordered topological and non-topological systems

Quantum phase transitions in disordered topological and non-topological systems 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. Here we obtain these phase diagrams using the machine learning method. We prepare thousands of wave functions in each phase, train the multi-layer convolutional neural network, and apply the neural network to determine the phase of the unknown systems from its wave function characteristics. Two- and three-dimensional Anderson transitions, as well as three dimensional topological insulators are discussed. We also compare this method with the conventional method.

[1] Tomoki Ohtsuki and Tomi Ohtsuki: J. Phys. Soc. Jpn. 85, 123706 (2016)
[2] Tomi Ohtsuki and Tomoki Ohtsuki: J. Phys. Soc. Jpn. 86, 044708 (2017)
[3] Tomohiro Mano and Tomi Ohtsuki: J. Phys. Soc. Jpn. 86, 113704 (2017)