Machine learning topological invariants of non-Hermitian systems

TL;DR

This paper demonstrates that neural networks can accurately predict topological invariants in non-Hermitian systems, facilitating the exploration of topological phases and transitions with minimal data.

Contribution

It introduces a machine learning approach to identify non-Hermitian topological invariants, enabling efficient analysis of complex topological phase diagrams.

Findings

Neural networks predict eigenvalue winding with nearly 100% accuracy.

Models successfully generalize to unseen phase regions.

Method applies to multiple non-Hermitian Hamiltonians.

Abstract

The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train neural networks to predict the winding of eigenvalues of four prototypical non-Hermitian Hamiltonians on the complex energy plane with nearly $100\%$ accuracy. Our demonstrations in the non-Hermitian Hatano-Nelson model, Su-Schrieffer-Heeger model and generalized Aubry-Andr\'e-Harper model in one dimension, and two-dimensional Dirac fermion model with non-Hermitian terms show the capability of the neural networks in exploring topological invariants and the associated topological phase transitions and topological phase diagrams in non-Hermitian systems. Moreover, the neural networks trained by a small data set in the phase diagram can successfully predict topological invariants in untouched phase regions. Thus, our work paves the way to revealing non-Hermitian topology with the machine learning toolbox.