Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore.
Phys Rev Lett. 2023 Jan 20;130(3):036601. doi: 10.1103/PhysRevLett.130.036601.
A remarkable breakthrough in topological phase classification is the establishment of the topological periodic table, which is mainly based on the classifying space analysis or K theory, but not based on concrete Hamiltonians that possess finite bands or arise in a lattice. As a result, it is still difficult to identify the topological phase of an arbitrary Hamiltonian; the common practice is, instead, to check the incomplete and still growing list of topological invariants one by one, very often by trial and error. Here, we develop unsupervised classifications of topological gapped systems with symmetries, and demonstrate the data-driven construction of the topological periodic table without a priori knowledge of topological invariants. This unsupervised data-driven strategy can take into account spatial symmetries, and further classify phases that were previously classified as trivial in the past. Our Letter introduces machine learning into topological phase classification and paves the way for intelligent explorations of new phases of topological matter.
拓扑相分类的一个显著突破是拓扑周期表的建立，它主要基于分类空间分析或 K 理论，而不是基于具有有限能带或出现在晶格中的具体哈密顿量。因此，仍然很难确定任意哈密顿量的拓扑相；通常的做法是，逐个检查不完整且仍在不断增长的拓扑不变量列表，这通常需要反复试验。在这里，我们发展了具有对称性的拓扑能隙系统的无监督分类，并展示了在没有拓扑不变量先验知识的情况下，数据驱动的拓扑周期表的构建。这种无监督的数据驱动策略可以考虑空间对称性，并进一步对以前被归类为平凡的相进行分类。我们的信件将机器学习引入拓扑相分类，并为智能探索拓扑物质的新相铺平了道路。
