The interface between Quantum Monte Carlo techniques and mean-field calculations for strongly correlated quantum many-body systems

Quantum Monte Carlo techniques are well established cutting-edge tools to unravel the behavior of quantum many-body systems. However, in most cases such methodologies need approximations due to the fermion sign problem, and such approximations are often uncontrollable. In particular, in the realm of ground state methodologies, a trial wave function, usually a mean-field wave function, is generally used to build an approximation. Recently, self-consistent procedures have been designed to systematically improve the trial wave function and to minimize the bias. We will show the results of systematic benchmarks relying on interfacing Hartree-Fock calculations with Constrained Path Quantum Monte Carlo calculations. In particular, we will focus on the Hubbard Hamiltonian as a guiding example and we will compute charge and magnetic correlations, as well as probes of electron localization.