QCD at non-zero density and canonical partition functions with Wilson fermions

TL;DR

This paper introduces a reduction method for Wilson Dirac fermions at non-zero chemical potential, enabling efficient computation of determinants and canonical partition functions independent of temporal lattice size.

Contribution

The authors develop a dimensionally reduced fermion matrix for Wilson fermions at finite density, simplifying determinant evaluation across chemical potentials.

Findings

Reduced fermion matrix size is independent of temporal extent

Determinant evaluation becomes computationally simpler

Exact projection to canonical partition functions achieved

Abstract

We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.