Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator

Abstract

I study the leading effects of discretization errors on the low energy part of the spectrum of the Hermitian Wilson-Dirac operator in infinite volume. The method generalizes that used to study the spectrum of the Dirac operator in the continuum, and uses partially quenched chiral perturbation theory for Wilson fermions. The leading-order corrections are proportional to a^2 (a being the lattice spacing). At this order I find that the method works only for one choice of sign of one of the three low energy constants describing discretization errors. If these constants have the relative magnitudes expected from large N_c arguments, then the method works if the theory has an Aoki phase for m of order a^2, but fails if there is a first-order transition. In the former case, the dependence of the gap and the spectral density on m and a^2 are determined. In particular, the gap is found to vanish more quickly as m_pi^2-> 0 than in the continuum. This reduces the region where simulations are safe from fluctuations in the gap.

44 pages, 16 figures (v2: reference added; v3: published version--typos corrected)

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Cited by in corpus (25)

• FLAG Review 2019
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Microscopic Spectrum of the Wilson Dirac Operator
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• QCD with light Wilson quarks on fine lattices (II): DD-HMC simulations and data analysis
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• On the consistency of the Aoki-phase
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• Chiral Symmetry Breaking on the Lattice
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory
• The Realization of the Sharpe-Singleton Scenario
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