Towards Multigrid Methods for Propagators of Staggered Fermions with Improved Averaging and Interpolation Operators

TL;DR

This paper develops improved multigrid methods for staggered fermion propagators, focusing on gauge covariant averaging kernels and coarse grid operators, with initial results in 2D SU(2) gauge fields.

Contribution

Introduces a numerically implemented Dirac-based averaging kernel and variational coarse grid operators for multigrid methods in lattice gauge theory.

Findings

Numerical implementation of Dirac-based averaging kernel

Initial results in 2D SU(2) gauge fields

Advocates C++ for future development

Abstract

A Dirac choice for the averaging kernel $C$ is implemented numerically. This improved kernel will be needed in gauge covariant multigrid computations for propagators of staggered fermions. Results for $C$ and the variational coarse grid operator will be given in 2-$d$ $SU(2)$ gauge fields. C++ is advocated for future algorithm development.