Winding expansion techniques for lattice QCD with chemical potential

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.