论文标题
无监督的机器学习和乐队拓扑
Unsupervised machine learning and band topology
论文作者
论文摘要
拓扑结构的研究是凝聚态物理及其他方面的研究领域。在这里，我们将该领域的最新进展与机器学习方面的发展相结合，这是另一个有趣的话题。具体而言，我们引入了一种无监督的机器学习方法，该方法搜索并检索了汉密尔顿人之间绝热变形的路径，从而根据其拓扑特性聚类。该算法是通用的，因为它不依赖于哈密顿量的特定参数化，并且很容易适用于任何对称类别。我们在一个和两个空间维度以及具有和不具有晶体对称性的不同对称类别中使用多个不同模型演示了该方法。因此，还显示了与一套普通指定的微不足道的原子绝缘子相比，如何诊断出微不足道和拓扑阶段。
The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest. Specifically, we introduce an unsupervised machine-learning approach that searches for and retrieves paths of adiabatic deformations between Hamiltonians, thereby clustering them according to their topological properties. The algorithm is general as it does not rely on a specific parameterization of the Hamiltonian and is readily applicable to any symmetry class. We demonstrate the approach using several different models in both one and two spatial dimensions and for different symmetry classes with and without crystalline symmetries. Accordingly, it is also shown how trivial and topological phases can be diagnosed upon comparing with a generally designated set of trivial atomic insulators.
