论文标题
以统计和机器学习方法为指导的工程拓扑阶段
Engineering Topological Phases Guided by Statistical and Machine Learning Methods
论文作者
论文摘要
搜索具有拓扑特性的材料是一项持续的努力。在本文中，我们提出了一种由机器学习技术支持的系统统计方法，该方法能够为通用晶格构建拓扑模型，而无需先前了解相图。通过从随机分布中抽样紧密结合参数向量，我们获得了我们用相应的拓扑指数标记的数据集。然后分析此标记的数据，以提取与拓扑分类最相关的那些参数并找到其最可能的值。我们发现参数的边际分布已经定义了拓扑模型。其他信息隐藏在参数之间的相关性中。在这里，我们作为概念证明了Haldane模型作为Altland-Zirnbauer（AZ）类Honeycomb晶格的原型拓扑绝缘子A类。该算法可直接适用于任何其他AZ类或格子类别，并且可以将其推广到相互作用系统。
The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. By sampling tight-binding parameter vectors from a random distribution we obtain data sets that we label with the corresponding topological index. This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values. We find that the marginal distributions of the parameters already define a topological model. Additional information is hidden in correlations between parameters. Here we present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A. The algorithm is straightforwardly applicable to any other AZ class or lattice and could be generalized to interacting systems.
