Quantum Monte Carlo techniques in the manifold of pairing wave functions for attractive Fermi gases

We present recent methodological innovations in the computational studies of strongly correlated attractive Fermi systems. Starting from the simplest form of auxiliary-field quantum Monte Carlo relying on Slater determinants, we discuss the possibility to use BCS wave functions as trial wave functions. In addition, we address the generalization needed whenever more complex forms of fermionic pairing are allowed (e.g., triplet pairing). We explore the possibility to interface quantum Monte Carlo and state-of-the-art Hartree-Fock-Bogoliubov calculations within a self-consistent scheme to systematically introduce correlations beyond mean field. We also discuss physical results, including a robust detection of a Larkin-Ovchinnikov phase possibly intertwined with non-trivial density modulations, and we show more recent intriguing results about topological phases in fermionic superfluids with spin-orbit coupling and Zeeman fields.