Spectrum of the Dirac Operator and Inversion Algorithms with Dynamical Staggered Fermions

TL;DR

This paper computes the spectra of the staggered Dirac operator in four-dimensional SU(2) gauge fields and investigates how eigenvalue distributions influence the efficiency of multigrid and conjugate gradient algorithms for fermion propagators.

Contribution

It provides complete spectral data of the Dirac operator in specific gauge fields and analyzes the impact of eigenvalue distributions on inversion algorithm performance.

Findings

Eigenvalue spectra are fully determined for the Dirac operator.

The performance of inversion algorithms correlates with eigenvalue distribution.

Insights into optimizing fermion propagator computations in lattice gauge theory.

Abstract

Complete spectra of the staggered Dirac operator $\Dirac$ are determined in four-dimensional $SU(2)$ gauge fields with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient algorithms for propagators with the distribution of the eigenvalues of~$\Dirac$.