Unsupervised learning of interacting topological phases from experimental observables  

作　　者：Li-Wei Yu Shun-Yao Zhang Pei-Xin Shen Dong-Ling Deng 

机构地区：[1]Theoretical Physics Division,Chern Institute of Mathematics and LPMC,Nankai University,Tianjin 300071,China [2]Center for Quantum Information,IIIS,Tsinghua University,Beijing 100084,China [3]Shanghai Qi Zhi Institute,41th Floor,AI Tower,No.701 Yunjin Road,Xuhui District,Shanghai 200232,China

出　　处：《Fundamental Research》2024年第5期1086-1091,共6页自然科学基础研究（英文版）

基　　金：supported by the National Natural Science Foundation of China(T2225008,12075128,11905108);support from the Shanghai Qi Zhi Institute.

摘　　要：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.

关 键 词：Unsupervised learning Topological phases Diffusion map Spectral function Ultracold atom 

分 类 号：O57[理学—粒子物理与原子核物理]