Linearized Auxiliary fields Monte Carlo: efficient sampling of the fermion sign

TL;DR

This paper presents a novel Monte Carlo method combining lattice Green function and auxiliary field techniques to efficiently compute exact ground state properties of the Hubbard model, overcoming some limitations of traditional approaches.

Contribution

The method integrates LGFMC and AFQMC to achieve unbiased zero-temperature results with faster convergence and reduced sign problem effects.

Findings

Accurate ground state energies for Hubbard model at U/t=4

Applicable to clusters with up to 100 sites

Eliminates Trotter approximation bias

Abstract

We introduce a method that combines the power of both the lattice Green function Monte Carlo (LGFMC) with the auxiliary field techniques (AFQMC), and allows us to compute exact ground state properties of the Hubbard model for U<~ 4t on finite clusters. Thanks to LGFMC one obtains unbiased zero temperature results, not affected by the so called Trotter approximation of the imaginary time propagator exp(- H t). On the other hand the AFQMC formalism yields a remarkably fast convergence in t before the fermion sign problem becomes prohibitive. As a first application we report ground state energies in the Hubbard model at U/t=4 with up to one hundred sites.