Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions

We study a system of hard-core bosons on a two-dimensional periodic honeycomb lattice subjected to an on-site potential with alternating signs along $y$-direction, using machine learning (ML) techniques. The model hosts a rich phase diagram consisting of six different phases including a charge density wave, a superfluid phase and two dimer insulator phases, one of which is also a weak topological insulator with zero Chern number but a non-trivial Berry phase [SciPost Phys. 10, 059 (2021)]. Using two distinct correlation functions computed via quantum Monte Carlo method, a relatively simple ML model is able to learn information from the various phases simultaneously and accurately predict their phase boundaries. By employing our ML model trained on the dataset obtained from the Hamiltonian without explicit interactions, we determine the phase structure of the system in the presence of nearest-neighbor interactions. Additionally, we investigate the robustness of the weak topological insulator phase against interactions by predicting the topological invariant, which is otherwise difficult to obtain.