A filtering technique for the temporally reduced matrix of the Wilson fermion determinant

TL;DR

This paper introduces a filtering method to efficiently compute low-energy eigenmodes of the temporally reduced Wilson fermion determinant matrix, enabling approximations that neglect ultraviolet contributions for larger volumes.

Contribution

A novel filtering technique for calculating low-energy eigenmodes of the reduced matrix, improving efficiency in evaluating the Wilson fermion determinant.

Findings

Efficient calculation of low-energy eigenmodes

Effective approximation by neglecting ultraviolet modes

Potential for larger volume simulations

Abstract

The Wilson fermion determinant can be written in the form of a series expansion in fugacity $\xi=\exp(\mu/T)$, provided that the eigenmodes of the temporally reduced operator are obtained. Since the calculation of all eigenmodes rapidly becomes prohibitive for larger volumes, we develop a method to calculate only the low-energy eigenmodes of the reduced matrix using a matrix filetering technique. This provides a basis for an approximation to neglect uninteresting ultraviolet contributions.