Global space-time update

TL;DR

This paper introduces a simplified and more efficient global space-time update scheme for the Stochastic Green Function (SGF) algorithm, enhancing simulation capabilities for sign-problem-free Hamiltonians, including complex models like the extended Bose-Hubbard.

Contribution

A new global space-time update method for the SGF algorithm that reduces auto-correlation times and simplifies implementation, enabling larger system simulations and ensemble flexibility.

Findings

Reduced auto-correlation times in simulations.

Effective handling of complex Hamiltonians.

Extended ensemble capabilities for SGF.

Abstract

The Stochastic Green Function (SGF) algorithm is able to simulate any Hamiltonian that does not suffer from the so-called "sign problem". We propose a new global space-time update scheme for the SGF algorithm which, in addition to being simpler than the previous formulation, reduces auto-correlation times. Using as a concrete example the extended Bose-Hubbard model and the complex Hamiltonian with six-site ring-exchange interactions which was recently studied in ArXiv:1206.2566v1, we present a comprehensive review of the SGF algorithm and the new updating scheme. Measurements of non-trivial physical quantities are presented in detail. While the SGF algorithm works in the canonical ensemble by nature, we give a simple extension that allows us to perform simulations in the grand-canonical ensemble too. We also discuss an optimized implementation which allows for access to large system sizes.