Winding expansion techniques for lattice QCD with chemical potential

Understand

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.