Machine Learning Disordered Topological Phases by Statistical Recovery of Symmetry

In this talk, we apply the artificial neural network (ANN) in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII [1]. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distribution individually is recovered statistically by taking an ensemble average. This enables us to classify the phases by the ANN that learned the quasiparticle distribution in the clean limit. The consistency of the result with the calculation by the transfer matrix method is shown. If all three of the Z2, trivial, and the thermal metal (ThM) phases appear in the clean limit, the machine can classify them with high confidence over the entire phase diagram. If only the former two phases are present, we find that the machine remains confused in the certain region, leading us to conclude the detection of the unknown phase which is eventually identified as the ThM. In our method, only the first moment of the quasiparticle distribution is used for input, but application to a wider variety of systems is expected by including higher moments.

[1] N. Yoshioka, Y. Akagi, and H. Katsura, arXiv:1709.05790.