Green function Monte Carlo with stochastic reconfiguration: An effective remedy for the sign problem

A recent technique, proposed to alleviate the "sign problem disease," is di scussed in detail. As is well known, the ground state of a given Hamiltonia n H can be obtained by applying the propagator e(-H tau) to a trial wave fu nction psi(T) and sampling statistically the state psi(tau)=e(-H tau)psi(T) for large imaginary time tau. However, the sign problem may appear in the simulation and such statistical propagation would be practically impossible without employing some approximation such as the "fixed node" (FN) one. Th e present method allows the improvement of the FN dynamics with a systemati c correction scheme. This is possible by the simple requirement that, after a short imaginary time propagation via the FN Hamiltonian, a number p of c orrelation functions can be further constrained to be exact by small pertur bations of the FN state, which is free from the sign problem. By iterating this procedure, the Monte Carlo average sign, which is almost zero when the re is a sign problem, remains stable and finite even for large tau. The pro posed algorithm is tested against exact diagonalization data available on f inite lattices. It is also shown, in some test cases, that the dependence o f the results upon the few parameters entering the stochastic technique can be very easily controlled, unless for exceptional cases.