  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.
