Machine learning of mirror skin effects in the presence of disorder

TL;DR

This paper demonstrates that the mirror skin effect in non-Hermitian systems with mirror symmetry remains robust against disorder that breaks the symmetry, using neural networks to predict and analyze localized edge states.

Contribution

It introduces a neural network approach to detect and analyze the mirror skin effect under disorder, revealing its robustness beyond symmetry-preserving conditions.

Findings

Neural network accurately predicts the presence of skin modes.

The skin effect persists despite mirror symmetry-breaking disorder.

Phase diagram of skin effect states is obtained using neural network predictions.

Abstract

Non-Hermitian systems with mirror symmetry may exhibit mirror skin effect which is the extreme sensitivity of the spectrum and eigenstates on the boundary condition due to the non-Hermitian topology protected by mirror symmetry. In this paper, we report that the mirror skin effect survives even against disorder which breaks the mirror symmetry. Specifically, we demonstrate the robustness of the skin effect by employing the neural network which systematically predicts the presence/absence of the skin modes, a large number of localized states around the edge. The trained neural network detects skin effects in high accuracy, which allows us to obtain the phase diagram. We also calculate the probability by the neural network for each of states. The above results are also confirmed by calculating the inverse participation ratio.