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 less than or similar to 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(-H tau). At the same time, the AFQMC formalism yields a remarkably fast convergence in tau 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.