Learning Disordered Topological Phases by Statistical Recovery of Symmetry

TL;DR

This paper demonstrates that neural networks can classify disordered topological phases by statistically recovering broken translational symmetry, achieving high accuracy and identifying unknown phases in complex quantum systems.

Contribution

It introduces a method using neural networks trained on clean limit distributions to classify disordered topological phases, incorporating statistical symmetry recovery.

Findings

Neural network classification aligns with transfer matrix and noncommutative geometry results.

High-confidence phase classification when all three phases are present.

Detection of an unknown phase as thermal metal when only two phases are present.

Abstract

In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. 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. By using this, we classify the phases by the artificial neural network that learned the quasiparticle distribution in the clean limit, and show that the result is totally consistent with the calculation by the transfer matrix method or noncommutative geometry approach. If all three phases, namely the $\mathbb{Z}_2$, trivial, and the thermal metal 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 thermal metal phase. 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 the inclusion of higher moments.