Unsupervised learning of interacting topological phases from experimental observables.

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.