Multigrid for Staggered Lattice Fermions

TL;DR

This paper develops a multigrid algorithm for staggered fermions in lattice field theory, addressing critical slowing down by introducing a spectral transformation based on Kähler-Dirac structure, with promising results in a 2D model and applicability to 4D QCD.

Contribution

It introduces a novel spectral transformation for multigrid methods tailored to staggered fermions, overcoming previous difficulties related to their anti-Hermitian structure.

Findings

Numerical results in 2D Schwinger model demonstrate effectiveness.

Method is dimension-agnostic and applicable to 4D lattice QCD.

Addresses critical slowing down in Krylov solvers.

Abstract

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.