  We implement a computational pipeline based on a recent machine learning
technique, namely the Topological Data Analysis (TDA), that has the capability
of extracting powerful information-carrying topological features. We apply such
a method to the study quantum phase transitions and, to showcase its validity
and potential, we exploit such a method for the investigation of two paramount
important quantum systems: the 2D 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.
