Efficient calculation of ground state properties of strongly correlated fermionic systems with BCS-Constrained-Path Auxiliary-Field Quantum Monte Carlo

We introduce an efficient and numerically stable technique to compute ground state correlation functions of strongly correlated physical systems within the Constrained-Path Auxiliary-Field Quantum Monte Carlo relying on a BCS trial wave function. Whenever the sign problem is absent, the methodology provides exact ground state properties. When the sign problem is present, on the other hand, the BCS wave function provides a powerful generalization of the usual Constrained-Path Auxiliary-Field Quantum Monte Carlo technique which relies on Slater Determinants. We present benchmark results for the attractive Hubbard model, comparing with exact diagonalization, including the case where a finite spin polarization is present. We also present results for the repulsive Hubbard model, in connection with d-wave pairing superconductivity.