Unsupervised Learning of Non-Hermitian Topological Phases

TL;DR

This paper develops an unsupervised machine learning method using diffusion maps to classify non-Hermitian topological phases, addressing challenges posed by the non-Hermitian skin effect.

Contribution

It introduces a novel approach for classifying non-Hermitian topological phases with diffusion maps, overcoming obstacles caused by the skin effect.

Findings

Diffusion maps can classify non-Hermitian topological phases.

Choosing on-site elements as input data circumvents the skin effect obstacle.

The method is validated through theoretical analysis and numerical simulations.

Abstract

Non-Hermitian topological phases bear a number of exotic properties, such as the non-Hermitian skin effect and the breakdown of conventional bulk-boundary correspondence. In this paper, we introduce an unsupervised machine learning approach to classify non-Hermitian topological phases based on diffusion maps, which are widely used in manifold learning. We find that the non-Hermitian skin effect will pose a notable obstacle, rendering the straightforward extension of unsupervised learning approaches to topological phases for Hermitian systems ineffective in clustering non-Hermitian topological phases. Through theoretical analysis and numerical simulations of two prototypical models, we show that this difficulty can be circumvented by choosing the on-site elements of the projective matrix as the input data. Our results provide a valuable guidance for future studies on learning non-Hermitian topological phases in an unsupervised fashion, both in theory and experiment.