Local Coarse-grained Approximation to Path Integral Monte Carlo Integration for Fermion Systems

An approximate treatment of exchange in finite-temperature path integral Monte Carlo simulations for fermions has been proposed. In this method, some of the fine details of density matrix due to permutations have been smoothed over or averaged out by using the coarse-grained approximation. The practical usefulness of the method is tested for interacting fermions in a three dimensional harmonic well. The results show that, the present method not only reduces the sign fluctuation of the density matrix, but also avoid the fermion system collapsing into boson system at low temperatures. The method is substantiated to be exact when applied to free particles.