The sign problem in quantum Monte Carlo simulations of the Hubbard model in a weak interaction region

Abstract

Determinant quantum Monte Carlo (QMC) simulations of fermion models normally face the sign problem, which has a strong dependence of the interaction strength, electron filling, temperature, lattice geometry and lattice size. It is useful to set up the data set of such dependence, to make it clear which parameter region is accessible or not. To supplement the previous study, here we report the behavior of the average sign in the weak interaction region, as functions of lattice geometry, lattice size, electron filling and temperature. Furthermore, we find that in the weak interaction region, for several interesting lattice geometries (except for the kagome lattice) the average sign gets improved when the lattice sizes increase, which is in contrast to the general understanding of the lattice size dependence of the average sign. This finding points out that when the sign problem is present in the weak interaction region, the simulation of a larger lattice size can be better under control.