论文标题
无监督的非热拓扑阶段的学习
Unsupervised Learning of Non-Hermitian Topological Phases
论文作者
论文摘要
非热拓扑阶段具有许多外来特性，例如非铁皮皮肤效应和常规散装对应关系的分解。在本文中，我们介绍了一种无监督的机器学习方法，以基于扩散图对非热拓扑阶段进行分类，该拓扑阶段被广泛用于多种学习中。我们发现，非铁皮皮肤效应将构成一个显着的障碍，从而使无监督学习方法的直接扩展到赫尔米尼系统的拓扑阶段无效，无效地聚集了非富裕拓扑阶段。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种困难。我们的结果为未来的研究以无监督的方式（理论上和实验）学习非高级拓扑阶段的未来研究提供了宝贵的指导。
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.
