Machine Learning of Mirror Skin Effects in the Presence of Disorder

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 inversed participation ratio.

Characterizing exceptional points using neural networks

“…-In summary, we have conveyed a data-centric approach to characterize the EPs. Notably, our approach goes beyond existing machinelearning applications in non-Hermitian physics, particularly in predicting non-Hermitian topological phases [32][33][34]39] and NHSE [37,38]. We have successfully demonstrated how ML techniques can be used to predict EPs and EP orders in various models with outstanding accuracy.…”

“…Non-Hermitian topological phases in phononics have been studied using manifold clustering [36]. Furthermore, Araki and co-authors have analysed NHSE in an ML framework [37]. Moreover, ML approaches have been recently explored to investigate various non-Hermitian experimental platforms.…”

Non-Hermitian topological phases: principles and prospects

“…Machine learning and artificial intelligence tools are growing in importance in physical sciences [367]. Very recently, there have been a handful of studies using both supervised and unsupervised machine learning approaches to characterize non-Hermitian topological phases [368][369][370][371][372]. Several connections to modern mathematics are also worth exploring in the context of non-Hermitian systems [373,374].…”