Machine learning topological phase transitions through local curvature

The topological order in materials is often calculated from the integration of a certain curvature function over the entire Brillouin zone. At topological phase transitions, the curvature function diverges and changes sign at certain high symmetry points in momentum space. These generic properties lead us to suggest a supervised machine learning scheme that uses only the curvature function at high symmetry points as input data to predict topological phase transitions. We use interacting models to demonstrate the efficiency of this method, which is shown to predict both the first- and second-order topological phase transitions caused by interactions with 100 percent accuracy in various models. The method further unveil the topological quantum multicriticality caused by many-body interactions. In particular, the electron-phonon interaction causes multicritical points where first- and second-order topological phase transitions intercept, and the first-order transition is accompanied by closing of the gap between the quasiparticle peak and the incoherent peak.