QUANTUM MONTE CARLO SIMULATION BY AUXILIARY FIELDS

The ground state properties of a many body hamiltonian H can be calculated by a recently developed technique, known as “the Projection Quantum Monte Carlo method”. Instead of simulating the many body system at finite temperature, one attempts to reach the zero temperature limit by applying to a trial wavefunction, suitably chosen, a many body propagator e^−Ht. For large enough t -t playing a role of an effective inverse temperature- the ground state component of the trial state is filtered out usually much faster than the corresponding finite temperature method. The Hubbard Stratonovich transformation allows to formulate the many body propagation of the trial state as that of sampling a distribution. This distribution is constructed by propagating the trial wavefunction under the influence of a one-body time dependent external field. However this distribution may be not positive definite, especially for large t, and serious problems occur when the average sign of the distribution is too small. We introduce a symmetric Hubbard Stratonovich transformation that in principle may solve this problem with large enough computer time. We also discuss how to apply the “Projection Quantum Monte Carlo” technique to the infinite U Hubbard model in a simple way.