Permutation zones and the fermion sign problem

Abstract

We present a new approach to the problem of alternating signs for fermionic many body Monte Carlo simulations. We demonstrate that the exchange of identical fermions is typically short-ranged even when the underlying physics is dominated by long distance correlations. We show that the exchange process has a maximum characteristic range of sqrt[2*(1-f)*beta*h] lattice sites, where beta is the inverse temperature, h is the hopping parameter, and f is the filling fraction. We introduce the notion of permutation zones, special regions of the lattice where identical fermions may interchange and outside of which they may not. Using successively larger permutation zones, one can extrapolate to obtain thermodynamic observables in regimes where direct simulation is impossible.