Spectral Properties of the Overlap Dirac Operator in QCD

Abstract

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at β= 5.85 and β= 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the ε-expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)^{4}. For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.

arXiv comment16 pages, 8 figures, final version published in JHEP

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Cited by in corpus (40)

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• Operator product expansion and quark condensate from Lattice QCD in coordinate space
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
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• Actions for dynamical fermion simulations: are we ready to go?
• Quark condensate in two-flavor QCD
• The Low-Lying Dirac Spectrum of Staggered Quarks
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• Distributions of Dirac Operator Eigenvalues
• Low-energy couplings of QCD from topological zero-mode wave functions
• Chiral properties of two-flavor QCD in small volume and at large lattice spacing
• Topological susceptibility from the overlap
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• Quark condensate in one-flavor QCD
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• Meson Correlation Functions in the epsilon-Regime
• Index Theorem and Random Matrix Theory for Improved Staggered Quarks
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• Overlap Hypercube Fermions in QCD
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• Simulating chiral quarks in the epsilon-regime of QCD
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