Transfer matrices and temporal factorization of the Wilson fermion determinant

TL;DR

This paper presents a method to factorize Wilson fermion determinants in lattice QCD using transfer matrices, enabling improved computational techniques for correlation functions and multi-level integration schemes.

Contribution

It introduces a novel factorization approach for Wilson fermion determinants via transfer matrices, with explicit constructions and potential applications.

Findings

Explicit transfer matrix constructions for Wilson fermions

Complete factorization of fermion determinants in temporal direction

Potential for improved estimators and multi-level algorithms

Abstract

When lattice QCD is formulated in sectors of fixed quark numbers, the canonical fermion determinants can be expressed explicitly in terms of transfer matrices. This in turn provides a complete factorization of the fermion determinants in temporal direction. Here we present a generic overview of this factorization, apply it to Wilson-type fermions and provide explicit constructions of the transfer matrices. Possible applications of the factorization include multi-level integration schemes and the construction of improved estimators for generic $n$-point correlation functions.