Sign problem and subsets in one-dimensional QCD

TL;DR

This paper introduces a subset method that effectively solves the sign problem in one-dimensional QCD at nonzero chemical potential, enabling numerical simulations and proposing extensions for multiple flavors.

Contribution

The paper presents a novel subset approach based on SU(3) center symmetry that completely solves the sign problem in 0+1 dimensional QCD for up to five flavors and extends to more flavors.

Findings

Successfully solves the sign problem in 0+1D QCD for up to five flavors

Proposes an extension of the subset method for more flavors

Provides preliminary results for higher-dimensional QCD subsets

Abstract

We present a subset method that solves the sign problem for QCD at nonzero quark chemical potential in 0+1 dimensions. The subsets of gauge configurations are constructed using the center symmetry of the SU(3) group. These subsets completely solve the sign problem for up to five flavors. For a larger number of flavors the sign problem slowly reappears, and we propose an extension of the subsets that also solves the sign problem for these cases. The subset method allows for numerical simulations of the model at nonzero chemical potential. We also present some preliminary results on subsets for QCD in two, three, and four dimensions.