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Multigrid algorithm for staggered lattice fermions

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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… Click to show full 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.

Keywords: algorithm staggered; staggered lattice; lattice fermions; multigrid algorithm

Journal Title: Physical Review D
Year Published: 2018

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