Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions

We propose a new projector quantum Monte-Carlo method to investigate the ground state of ultracold fermionic atoms modeled by a lattice Hamiltonian with on-site interaction. The many-body state is reconstructed from Slater determinants that randomly evolve in imaginary-time according to a stochastic mean-field motion. The dynamics prohibits the crossing of the exact nodal surface and no sign problem occurs in the Monte-Carlo estimate of observables. The method is applied to calculate ground-state energies and correlation functions of the repulsive two-dimensional Hubbard model. Numerical results for the unitary Fermi gas validate simulations with nodal constraints.