Learning quantum phase transitions through topological data analysis

Abstract

We implement a computational pipeline based on a recent machine learning technique, namely, topological data analysis (TDA), that has the capability of extracting powerful information-carrying topological features. We apply such a method to study quantum phase transitions, and to showcase its validity and potential, we exploit such a method for the investigation of two quantum systems of paramount importance: the two-dimensional periodic Anderson model and the Hubbard model on the honeycomb lattice, both cases on the half filling. To this end, we have performed unbiased auxiliary-field quantum Monte Carlo simulations, feeding the TDA with snapshots of the Hubbard-Stratonovich fields through the course of the simulations. The quantum critical points obtained from TDA agree quantitatively well with the existing literature, therefore suggesting that this technique could be used to investigate quantum systems where the analysis of the phase transitions is still a challenge.