Systematic errors of L\"uscher's fermion method and its extensions

TL;DR

This paper investigates the systematic errors in L"uscher's fermion method for dynamical Wilson quarks, analyzing error behavior, improvements via variants, and proposing an exact algorithm with a Metropolis test.

Contribution

It provides a detailed analysis of errors in L"uscher's formulation, introduces a non-hermitian variant for better approximation, and proposes an exact algorithm using a Metropolis test.

Findings

Optimal cutoff window identified for minimal errors.

Error decreases exponentially with more boson families.

Non-hermitian variant enables odd number of flavors.

Abstract

We study the systematic errors of L\"uscher's formulation of dynamical Wilson quarks and some of its variants, in the weak and strong coupling limits, and on a sample of small configurations at finite $\beta$. We confirm the existence of an optimal window in the cutoff parameter $\varepsilon$, and the exponential decrease of the error with the number of boson families. A non-hermitian variant improves the approximation further and allows for an odd number of flavors. A simple and economical Metropolis test is proposed, which makes the algorithm exact.