Winding expansion techniques for lattice QCD with chemical potential

TL;DR

This paper introduces a method to decompose the lattice fermion determinant in lattice QCD with chemical potential into winding sectors, enabling more efficient calculations of fixed quark number partition functions.

Contribution

It analytically derives a winding sector decomposition of the fermion determinant and explores its applications for faster computation of canonical partition functions.

Findings

Decomposition into winding sectors is feasible and well-defined.

The method enables dimensional reduction in Fourier transforms.

Power series expansion improves computational efficiency.

Abstract

We analytically derive a decomposition of the lattice fermion determinant for Wilson's Dirac operator with chemical potential into winding sectors, i.e., factors with a fixed number of quarks. Dividing the lattice into four domains, the determinant is factorized into terms which can be classified with respect to the winding number of the closed loops they consist of. The individual factors are expressed in terms of subdeterminants and propagators on the domains of the lattice. We numerically analyze properties of the factorization formula and discuss two applications for the determination of canonical partition functions with a fixed quark number: A speedup for the Fourier transformation technique through a dimensional reduction, and a power series expansion.