Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator

Details Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator

1999-01-21

arxiv.org/abs/hep-lat/9901015v1

Phys.Rev. D60 (1999) 034502

Physics

High Energy Physics

High Energy Physics - Lattice

19 pages revtex with 9 postscript figures included by epsf

Scientific paper

10.1103/PhysRevD.60.034502

We investigate the approach to the continuum limit of the spectrum of the Hermitian Wilson-Dirac operator in the supercritical mass region for pure gauge SU(2) and SU(3) backgrounds. For this we study the spectral flow of the Hermitian Wilson-Dirac operator in the range $0\le m\le 2$. We find that the spectrum has a gap for $0 < m \le m_1$ and that the spectral density at zero, $\rho(0;m)$, is non-zero for $m_1\le m\le 2$. We find that $m_1\to 0$ and, for $m \ne 0, \rho(0;m)\to 0$ (exponential in the lattice spacing) as one goes to the continuum limit. We also compute the topological susceptibility and the size distribution of the zero modes. The topological susceptibility scales well in the lattice spacing for both SU(2) and SU(3). The size distribution of the zero modes does not appear to show a peak at a physical scale.

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