  Within the ground-state auxiliary-field quantum Monte Carlo technique, we
introduce discrete Hubbard-Stratonovich transformations (HSTs) that are
suitable also 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
as a generalization of the discrete HSTs by Hirsch [J. E. Hirsch, Phys. Rev. B
28, 4059 (1983)] or a compactification of the shifted-contour auxiliary-field
Monte Carlo formalism by Rom et al. [N. Rom et al., Chem. Phys. Lett. 270, 382
(1997)]. An improvement of the acceptance ratio is found for a real auxiliary
field, while an improvement of the average sign is found for a pure-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.
