Tackling the sign problem with a moment expansion and application to Heavy dense QCD

TL;DR

This paper introduces a new moment expansion method to address the sign problem in Heavy-Dense QCD, demonstrating rapid convergence and effectiveness in challenging regimes.

Contribution

A systematic moment expansion approach for calculating the phase factor in Heavy-Dense QCD, improving accuracy in regions with severe sign problems.

Findings

The moment expansion converges quickly.

The method performs well in strong sign problem regions.

Comparison with exact results shows high accuracy.

Abstract

Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem in quantum field theory. Besides its physical applications, HDQCD is relatively easy to implement numerically: the fermionic degrees of freedom are integrated out, and the fermion determinant factorises into local ones. The theory has a sign problem, the severeness of which depends on the value of the chemical potential, which makes this theory ideal to test the reach of new algorithms. We use the LLR approach to obtain the probability distribution of the phase of the fermion determinant. Our goal is the calculation of the phase factor expectation value, which appears as Fourier transform of this probability distribution. We here propose a new and systematic moment expansion for this phase factor. We compare the answer from the moment expansion order by order with the exact answer. We find that this expansion converge quickly and works very well in the strong sign problem region.