Self-Attention Assistant Classification of Non-Hermitian Phases in Two-Dimensional Lattice

Abstract

Classification of the non-Hermitian phases in high-dimensional lattice becomes challenging due to interplay of the band topology and non-Hermiticity. The significant increase in data dimensions and the number of categories has rendered traditional supervised learning and unsupervised manifold learning failed. Here, we propose the self-attention assistant machine learning for clustering non-Hermitian phases in two-dimensional lattice. By incorporating the self-attention mechanism, the model can effectively capture long-range dependencies and important patterns, resulting in a more compact and information-rich latent space. It can achieve Altland-Zirnbauer classification with Bloch vector dataset and distinguish the phases of eigenstates' localized behavior with the competition between non-Hermitian skin effect and topological localization. Our results provide a general method for characterizing non-Hermitian phases in two-dimensional lattice via machine learning.