Yu Li-Wei, Zhang Shun-Yao, Shen Pei-Xin, Deng Dong-Ling
Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.
Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China.
Fundam Res. 2023 Jan 20;4(5):1086-1091. doi: 10.1016/j.fmre.2022.12.016. eCollection 2024 Sep.
Classifying topological phases of matter with strong interactions is a notoriously challenging task and has attracted considerable attention in recent years. In this paper, we propose an unsupervised machine learning approach that can classify a wide range of symmetry-protected interacting topological phases directly from the experimental observables and without a priori knowledge. We analytically show that Green's functions, which can be derived from spectral functions that can be measured directly in an experiment, are suitable for serving as the input data for our learning proposal based on the diffusion map. As a concrete example, we consider a one-dimensional interacting topological insulators model and show that, through extensive numerical simulations, our diffusion map approach works as desired. In addition, we put forward a generic scheme to measure the spectral functions in ultracold atomic systems through momentum-resolved Raman spectroscopy. Our work circumvents the costly diagonalization of the system Hamiltonian, and provides a versatile protocol for the straightforward and autonomous identification of interacting topological phases from experimental observables in an unsupervised manner.
对具有强相互作用的物质拓扑相进行分类是一项极具挑战性的任务，近年来引起了广泛关注。在本文中，我们提出了一种无监督机器学习方法，该方法可以直接从实验可观测量中对各种对称性保护的相互作用拓扑相进行分类，且无需先验知识。我们通过分析表明，格林函数可从实验中直接测量的谱函数导出，适用于作为基于扩散映射的学习方法的输入数据。作为一个具体例子，我们考虑一维相互作用拓扑绝缘体模型，并通过大量数值模拟表明，我们的扩散映射方法能如预期般工作。此外，我们提出了一种通过动量分辨拉曼光谱在超冷原子系统中测量谱函数的通用方案。我们的工作规避了系统哈密顿量的昂贵对角化过程，并提供了一种通用协议，用于以无监督方式从实验可观测量中直接且自主地识别相互作用拓扑相。
