Sufficient condition for absence of the sign problem in the fermionic quantum Monte Carlo algorithm

Quantum Monte Carlo (QMC) simulations involving fermions have a notorious sign problem. Some well-known exceptions to the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC algorithm [C. Wu, J. Hu, and S. Zhang, Phys. Rev. Lett. 91, 186402 (2003)] has been found in which the fermion determinant may not necessarily be factorizable, but can instead be expressed as a product of complex conjugate pairs of eigenvalues, thus eliminating the sign problem for a much wider class of models. In this paper, we present the general conditions for the applicability of this algorithm and point out that it is deeply related to the time-reversal symmetry of the fermion matrix. We apply this method to various models of strongly correlated systems at all doping levels and lattice geometries, and show that many phases can be simulated without the sign problem.