Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations

Within the ground-state auxiliary-field quantum Monte Carlo technique, we introduce discrete Hubbard-Stratonovich transformations (HSTs) that are also suitable for spatially inhomogeneous trial functions. The discrete auxiliary fields introduced here are coupled to local spin or charge operators fluctuating around their Hartree-Fock values. The formalism can be considered a generalization of the discrete HSTs by J. E. Hirsch [Phys. Rev. B 28, 4059 (1983)PRBMDO0163-182910.1103/PhysRevB.28.4059] or a compactification of the shifted-contour auxiliary-field Monte Carlo formalism by N. Rom et al. [Chem. Phys. Lett. 270, 382 (1997)CHPLBC0009-261410.1016/S0009-2614(97)00370-9]. An improvement of the acceptance ratio is found for a real auxiliary field, while an improvement of the average sign is found for a purely imaginary auxiliary field. Efficiencies of the different HSTs are tested in the single-band Hubbard model at and away from half filling by studying the staggered magnetization and energy expectation values, respectively.