Eigenvalue spectrum of massless Dirac operators on the lattice

Abstract

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.

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

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• Random Matrix Theories in Quantum Physics: Common Concepts
• Exactly massless quarks on the lattice
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• More about exactly massless quarks on the lattice
• The index theorem in QCD with a finite cut-off
• Vector like gauge theories with almost massless fermions on the lattice
• Lattice QCD without tuning, mixing and current renormalization
• Prospects for perfect actions
• A practical implementation of the Overlap-Dirac operator
• Microscopic universality in the spectrum of the lattice Dirac operator
• Spectral flow, condensate and topology in lattice QCD
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• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Dirac Operator Spectra from Finite-Volume Partition Functions
• Fixed point action for the massless lattice Schwinger model
• Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions
• Microscopic universality with dynamical fermions
• Crossover to Non-universal Microscopic Spectral Fluctuations in Lattice Gauge Theory
• Statistical properties at the spectrum edge of the QCD Dirac operator
• Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
• Chiral properties of the fixed point action of the Schwinger model
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• A fixed-point action for the lattice Schwinger model

Cited by in corpus (36)

• Random Matrix Theory and Chiral Symmetry in QCD
• Approximate Ginsparg-Wilson fermions: A first test
• Scaling tests with dynamical overlap and rooted staggered fermions
• A variant approach to the overlap action
• Staggered versus overlap fermions: a study in the Schwinger model with $N_f=0,1,2$
• Simple Observables from Fat Link Fermion Actions
• Actions for dynamical fermion simulations: are we ready to go?
• The Scaling of Exact and Approximate Ginsparg-Wilson Fermions
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• A comprehensive picture of topological excitations in finite temperature lattice QCD
• Effective Low Energy Theories and QCD Dirac Spectra
• Spectral Properties of the Overlap Dirac Operator in QCD
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Convergence Rate and Locality of Improved Overlap Fermions
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Staggered Fermions and Gauge Field Topology
• Quark spectra and light hadron phenomenology from overlap fermions with improved gauge field action
• Schwinger Model with the Overlap-Dirac Operator: exact results versus a physics motivated approximation
• Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite Temperature
• Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
• Dirac Spectra of 2-dimensional QCD-like theories
• Effects of Topology in the Dirac Spectrum of Staggered Fermions
• Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice
• Chiral condensate in the quenched Schwinger model
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Divergent chiral condensate in the quenched Schwinger model
• Fake symmetry transitions in lattice Dirac spectra
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Features of a 2d Gauge Theory with Vanishing Chiral Condensate
• Bound states for Overlap and Fixed Point Actions close to the chiral limit
• Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator
• Looking for Effects of Topology in the Dirac Spectrum of Staggered Fermions
• Randomness on the Lattice
• Comparing lattice Dirac operators with Random Matrix Theory
• Finite-Volume Scaling of the Quenched Chiral Condensate