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

## TL;DR

This paper evaluates a new class of discrete Hubbard-Stratonovich transformations within auxiliary-field quantum Monte Carlo methods, improving efficiency and accuracy in simulating the Hubbard model, especially for inhomogeneous systems.

## Contribution

It introduces a generalized discrete Hubbard-Stratonovich transformation suitable for inhomogeneous trial functions, enhancing Monte Carlo sampling efficiency and accuracy.

## Key findings

- Improved acceptance ratio with real auxiliary fields.
- Enhanced average sign with pure-imaginary auxiliary fields.
- Effective in simulating Hubbard model at various fillings.

## Abstract

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.