Positivity of center subsets for QCD

TL;DR

This paper advances a subset-based approach to address the sign problem in lattice QCD at nonzero chemical potential, demonstrating positivity of subset weights in larger lattices and providing initial numerical results in two dimensions.

Contribution

It extends the positivity proof of subset weights from 0+1 dimensions to larger lattices and introduces a method to reintroduce the gauge action via reweighting.

Findings

Positivity of subset weights proven for two-site temporal lattices.

Numerical evidence suggests positivity persists on larger lattices.

Initial quark number results obtained in two-dimensional simulations.

Abstract

We further pursue an approach to the sign problem of quantum chromodynamics at nonzero chemical potential, in which configurations of the lattice path integral are gathered into subsets. In the subset construction we multiply each temporal link by center elements independently and in a first step neglect the gauge action. The positivity of the subset weights -- shown for 0+1 dimensions in an earlier study -- extends to larger lattices: for two sites in the temporal direction and arbitrary spatial extent we give a proof of the positivity by decomposing the subset weight in positive summands. From numerical evidence we conjecture that the positivity persists on larger lattices and that the gauge action can be reintroduced through mild reweighting. First results on the quark number obtained with this method in two dimensions are shown as well.