Linearized auxiliary fields Monte Carlo technique: Efficient sampling of the fermion sign

We introduce a method that combines the power of both the lattice Green' function Monte Carlo (LGFMC) with the auxiliary field quantum Monte Carlo (AFQMC) techniques, and allows us to compute exact ground-state properties of the Hubbard model for U≲4t on finite clusters. Thanks to LGFMC, one obtains unbiased zero temperature results, not affected by the so-called Trotter approximation of the imaginary time propagator e−Hτ. At the same time, the AFQMC formalism yields a remarkably fast convergence in τ before the fermion sign problem becomes prohibitive. As an application we report ground-state energies of the Hubbard model at U/t=4 with up to 100 sites.