Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings

Abstract

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index of the Wilson Dirac operator. The low-energy constants of Wilson chiral Perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.

48 pages, 8 figures,v2 minor corrections same version as published in PRD

References in corpus (10)

• Universality of the topological susceptibility in the SU(3) gauge theory
• Random matrices beyond the Cartan classification
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• The epsilon regime with Wilson fermions
• Observations on the Wilson fermions in the epsilon regime
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Localized eigenmodes of the overlap operator and their impact on the eigenvalue distribution
• QCD with two flavors of Wilson fermions: The QCD vacuum, the Aoki vacuum and other vacua

Cited by in corpus (51)

• Lattice QCD with open boundary conditions and twisted-mass reweighting
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Large-N reduction in QCD with two adjoint Dirac fermions
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory
• The Realization of the Sharpe-Singleton Scenario
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Overlap valence quarks on a twisted mass sea: a case study for mixed action Lattice QCD
• The Microscopic Twisted Mass Dirac Spectrum
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• The Heisenberg XX spin chain and low-energy QCD
• Determining low-energy constants in partially quenched Wilson chiral perturbation theory
• Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors
• Vacuum alignment and lattice artifacts: Wilson fermions
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Complex Langevin simulations of a finite density matrix model for QCD
• Baryon chiral perturbation theory with Wilson fermions up to $\mathcal{O}(a^2)$ and discretization effects of latest $n_f=2+1$ LQCD octet baryon masses
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Baryon Number Dirac Spectrum in QCD
• Spectrum of QCD with one flavor: A window for supersymmetric dynamics
• Kondo effect with Wilson fermions
• On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix
• Universality Conjecture for all Airy, Sine and Bessel Kernels in the Complex Plane
• Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor
• Elucidating the Vacuum Structure of the Aoki Phase
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
• Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues
• Universal Distribution of Would-be Topological Zero Modes in Coupled Chiral Systems
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion
• Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator
• Large-$N_c$ gauge theory and chiral random matrix theory
• Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories
• Universal distributions from non-Hermitian Perturbation of Zero-Modes
• Generalised unitary group integrals of Ingham-Siegel and Fisher-Hartwig type
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$
• Chiral random matrix theory for colorful quark-antiquark condensates
• Discretization effects in $N_c=2$ QCD and Random Matrix Theory
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Universal Broadening of Zero Modes: A General Framework and Identification
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• The Effect of the Low Energy Constants on the Spectral Properties of the Wilson Dirac Operator
• One Flavour QCD as an analogue computer for SUSY
• New term in effective field theory at fixed topology