Auxiliary-Field Quantum Monte Carlo methods in the manifold of Hartree-Fock-Bogoliubov wave functions

We present innovative implementations of quantum Monte Carlo techniques to compute ground state correlations when complex pairing order parameters are present or expected. We show how to generalize the well-established auxiliary-field quantum Monte Carlo method, which is a method of choice for lattice models in condensed matter physics, to study hamiltonians which include pairing terms which break U(1) symmetry. The plan is to be able to find accurate non-perturbative results for pairing order parameters in cold atomic Fermi systems with spin-orbit coupling and Zeeman fields as well as in lattice models for unconventional superconductors. We discuss the complexity and numerical stability of the algorithm and we present applications to small systems, where we are able to compare the predictions with exact diagonalization.