Subsets and the canonical partition functions

TL;DR

This paper explains how the subset sum method addresses the sign problem in chiral random matrix theory by isolating the zero quark charge sector, which yields the full partition function independent of chemical potential.

Contribution

It demonstrates that the subset sum projects out the zero quark charge sector, providing a physical understanding of the subset solution to the sign problem in chiral random matrix theory.

Findings

Subset sum projects out zero quark charge determinants.

Zero quark charge sector yields the full partition function.

Partition function is independent of chemical potential in this sector.

Abstract

We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: The subset sum is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition function is independent of the chemical potential, the zero quark charge sector provides the full result.