Reducing the Sign Problem with simple Contour Deformation

TL;DR

This paper introduces a simple contour deformation method using constant imaginary offsets to mitigate the sign problem in Hubbard model simulations, enabling more efficient calculations of complex systems.

Contribution

The authors propose a novel, straightforward contour deformation technique that significantly reduces the sign problem without slowing down Hybrid Monte Carlo algorithms.

Findings

Significantly improved results for C20 and C60 fullerenes

Complete elimination of the sign problem at high chemical potential with optimal offset

Enhanced computational accessibility for previously intractable systems

Abstract

We apply constant imaginary offsets to the path integral for a reduction of the sign problem in the Hubbard model. These simple transformations enhance the quality of results from HMC calculations without compromising the speed of the algorithm. This method enables us to efficiently calculate systems that are otherwise inaccessible due to a severe sign problem. To support this claim, we present observables of the C20 and C60 fullerenes. Furthermore, we demonstrate that at a certain offset, the sign problem is completely lifted in the limit of large chemical potential.