Unsupervised Learning of Non-Hermitian Topological Phases,Physical Review Letters

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Unsupervised Learning of Non-Hermitian Topological Phases
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-06-16 , DOI: 10.1103/physrevlett.126.240402
Li-Wei Yu ₁ , Dong-Ling Deng _{1,

2}

Affiliation

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 Letter, 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.

中文翻译：

非厄米拓扑相的无监督学习

非厄米拓扑相具有许多奇异的特性，例如非厄米趋肤效应和常规体边界对应的破坏。在这封信中，我们介绍了一种无监督的机器学习方法，用于基于广泛用于流形学习的扩散图对非厄米拓扑相进行分类。我们发现非 Hermitian 趋肤效应将构成一个显着的障碍，使得 Hermitian 系统的拓扑阶段的无监督学习方法的直接扩展在非 Hermitian 拓扑阶段的聚类中无效。通过对两个原型模型的理论分析和数值模拟，我们表明可以通过选择投影矩阵的“现场”元素作为输入数据来规避这一困难。

更新日期：2021-06-16

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