Idealized Multigrid Algorithm for Staggered Fermions

TL;DR

This paper investigates an idealized multigrid algorithm for staggered fermions, demonstrating its ability to preserve criticality and reduce critical slowing, though it is not practical for real-world applications.

Contribution

It introduces an idealized multigrid approach that maintains criticality under coarsening, unlike the Galerkin method, providing fundamental insights into multigrid algorithms for fermions.

Findings

Preserves criticality under coarsening

Reduces relaxation times significantly

Not practical for production runs

Abstract

An idealized multigrid algorithm for the computation of propagators of staggered fermions is investigated. Exemplified in four-dimensional $SU(2)$ gauge fields, it is shown that the idealized algorithm preserves criticality under coarsening. The same is not true when the coarse grid operator is defined by the Galerkin prescription. Relaxation times in computations of propagators are small, and critical slowing is strongly reduced (or eliminated) in the idealized algorithm. Unfortunately, this algorithm is not practical for production runs, but the investigations presented here answer important questions of principle.