Multigrid for propagators of staggered fermions in four-dimensional $SU(2)$ gauge fields

TL;DR

This paper investigates multigrid methods for calculating staggered fermion propagators in four-dimensional SU(2) gauge fields, finding that current variational approaches are not yet competitive with conjugate gradient algorithms.

Contribution

It evaluates the effectiveness of multigrid methods with Laplacian restriction operators for fermion propagators in non-Abelian gauge fields, highlighting current limitations.

Findings

Multigrid methods are theoretically applicable to disordered systems.

Current variational multigrid methods are not competitive with conjugate gradient algorithms.

Numerical results are provided for SU(2) gauge field propagators.

Abstract

Multigrid (MG) methods for the computation of propagators of staggered fermions in non-Abelian gauge fields are discussed. MG could work in principle in arbitrarily disordered systems. The practical variational MG methods tested so far with a ``Laplacian choice'' for the restriction operator are not competitive with the conjugate gradient algorithm on lattices up to $18^4$. Numerical results are presented for propagators in $SU(2)$ gauge fields.