Eigenvalue spectrum of massless Dirac operators on the lattice

Details Eigenvalue spectrum of massless Dirac operators on the lattice Eigenvalue spectrum of massless Dirac operators on the lattice

1998-12-19

arxiv.org/abs/hep-lat/9812018v2

Nucl.Phys. B549 (1999) 364-388

Physics

High Energy Physics

High Energy Physics - Lattice

13 figures, 33 pages; minor changes, update to version accepted for publication

Scientific paper

10.1016/S0550-3213(99)00162-5

We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action recently proposed by Neuberger. Both actions show the remnant of chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation. We check this issue for practical implementations, also evaluating the fermion condensate in a finite volume by a subtraction procedure. Moreover, we investigate the distribution of the eigenvalues of a properly defined anti-hermitian lattice Dirac operator, studying the statistical properties at the low lying edge of the spectrum. The comparison with the predictions of chiral Random Matrix Theory enables us to obtain an estimate of the infinite volume fermion condensate.

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