Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions

Abstract

Complete spectra of the staggered Dirac operator $\Dirac$ are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An attempt is made to relate the performance of multigrid (MG) and conjugate gradient (CG) algorithms for propagators with the distribution of the eigenvalues of~$\Dirac$. The convergence of the CG algorithm is determined only by the condition number~$\kappa$ and by the lattice size. Since~$\kappa$'s do not vary significantly when quarks become dynamic, CG convergence in unquenched fields can be predicted from quenched simulations. On the other hand, MG convergence is not affected by~$\kappa$ but depends on the spectrum in a more subtle way.

19 pages, 8 figures, HUB-IEP-94/12 and KL-TH 19/94; comes as a uuencoded tar-compressed .ps-file

References in corpus (7)

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• Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
• Systematics of Staggered Fermion Spectral Properties and Topology
• On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations
• Topological Aspects of Fermions on Hyperdiamond
• An Exact Algorithm for Any-flavor Lattice QCD with Kogut-Susskind Fermion
• Neural-network preconditioners for solving the Dirac equation in lattice gauge theory
• Universal and non-universal behavior in Dirac spectra
• Study of Cullum's and Willoughby's Lanczos method for Wilson fermions