论文标题
机器学习拓扑不变式
Machine learning topological invariants of non-Hermitian systems
论文作者
论文摘要
最近，通过机器学习方法对拓扑特性的研究引起了极大的兴趣。在这里，我们建议机器学习在非热门系统中独特的拓扑不变性。具体而言，我们训练神经网络，以预测复杂能量平面上四个原型非汉密尔顿的特征值的绕组，其精度接近100美元。我们在一个非热的Hatano-Nelson模型，Su-Schrieffer-Heeger模型中的演示和一般化的Aubry-André-Harper模型以及具有非热门术语的二维Dirac Fermion模型，显示了神经网络在探索拓扑相位和近端的拓扑相交方面的能力。此外，通过相图中的小数据集训练的神经网络可以成功预测未触及的相位区域中的拓扑不变性。因此，我们的作品为使用机器学习工具箱揭示非热拓扑的方式铺平了道路。
The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train neural networks to predict the winding of eigenvalues of four prototypical non-Hermitian Hamiltonians on the complex energy plane with nearly $100\%$ accuracy. Our demonstrations in the non-Hermitian Hatano-Nelson model, Su-Schrieffer-Heeger model and generalized Aubry-André-Harper model in one dimension, and two-dimensional Dirac fermion model with non-Hermitian terms show the capability of the neural networks in exploring topological invariants and the associated topological phase transitions and topological phase diagrams in non-Hermitian systems. Moreover, the neural networks trained by a small data set in the phase diagram can successfully predict topological invariants in untouched phase regions. Thus, our work paves the way to revealing non-Hermitian topology with the machine learning toolbox.
