A Study of Practical Implementations of the Overlap-Dirac Operator in Four Dimensions

Abstract

We study three practical implementations of the Overlap-Dirac operator $D_o=(1/2)[1+{\gamma }_5\epsilon (H_w)]$ in four dimensions. Two implementations are based on different representations of $\epsilon (H_w)$ as a sum over poles. One of them is a polar decomposition and the other is an optimal fit to a ratio of polynomials. The third one is obtained by representing $\epsilon (H_w)$ using Gegenbauer polynomials and is referred to as the fractional inverse method. After presenting some spectral properties of the Hermitian operator $H_o={\gamma }_5{D}_o$, we study its spectrum in a smooth SU(2) instanton background with the aim of comparing the three implementations of $D_o$. We also present some results in SU(2) gauge field backgrounds generated at $\beta =2.5$ on an $8^4$ lattice. Chiral properties have been numerically verified.

23 pages latex with 9 postscript figures included by epsf. Some change in referencing and one figure modified

References in corpus (4)

• Exactly massless quarks on the lattice
• Vector like gauge theories with almost massless fermions on the lattice
• The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds
• Monte Carlo evaluation of a fermion number violating observable in 2D

Cited by in corpus (80)

• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Locality properties of Neuberger's lattice Dirac operator
• Domain wall QCD with physical quark masses
• Variants of fattening and flavor symmetry restoration
• Light Hadron Masses from Lattice QCD
• Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds
• Numerical techniques for lattice QCD in the $\epsilon$--regime
• Quark spectra, topology and random matrix theory
• A variant approach to the overlap action
• Non-equilibrium study of the Chiral Magnetic Effect from real-time simulations with dynamical fermions
• Overlap Valence on 2+1 Flavor Domain Wall Fermion Configurations with Deflation and Low-mode Substitution
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Light Quark Masses with Overlap Fermions in Quenched QCD
• Chiral Condensate in the Deconfined Phase of Quenched Gauge Theories
• Overlap Quark Propagator in Landau Gauge
• Physics issues in simulations with dynamical overlap fermions
• Simple Observables from Fat Link Fermion Actions
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• The Scaling of Exact and Approximate Ginsparg-Wilson Fermions
• Lattice QCD with the Overlap-Dirac Operator: Its $\Lambda$ Parameter, and One-Loop Renormalization of Fermionic Currents
• One-loop renormalization of fermionic currents with the overlap-Dirac operator
• Center Vortices and Chiral Symmetry Breaking in SU(2) Lattice Gauge Theory
• Local Chirality of Low-Lying Dirac Eigenmodes and the Instanton Liquid Model
• Accelerated Overlap Fermions
• Numerical Methods for the QCD Overlap Operator:III. Nested Iterations
• The Kaon B-parameter from Quenched Domain-Wall QCD
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Algorithms for Lattice QCD with Dynamical Fermions
• Numerical Methods for the QCD Overlap Operator IV: Hybrid Monte Carlo
• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• Domain Wall Fermions with Exact Chiral Symmetry
• Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators with Overlap Fermions
• Chiral Properties of Pseudoscalar Mesons on a Quenched $20^4$ Lattice with Overlap Fermions
• Exact local fermionic zero modes
• Are Topological Charge Fluctuations in QCD Instanton Dominated?
• Lambda-parameter of lattice QCD with the overlap-Dirac operator
• Topology and chiral symmetry breaking in SU(N) gauge theories
• Tests of the lattice index theorem
• Light hadron and diquark spectroscopy in quenched QCD with overlap quarks on a large lattice
• Perturbative renormalization of moments of quark momentum, helicity and transversity distributions with overlap and Wilson fermions
• Lanczos Approach to the Inverse Square Root of a Large and Sparse Matrix
• Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions
• B_K from quenched QCD with exact chiral symmetry
• Schwinger Model with the Overlap-Dirac Operator: exact results versus a physics motivated approximation
• Quenched Results for Light Quark Physics with Overlap Fermions
• Exact Zero-Modes of the Compact QED Dirac Operator
• Topological Phases in Neuberger-Dirac operator
• Recent Developments of Domain-wall/Overlap Fermions for Lattice QCD
• Numerical study of lattice index theorem usingimproved cooling and overlap fermions
• Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects
• Approximation Theory for Matrices
• Improved Pseudofermion Approach for All-Point Propagators
• Fermion-scalar interactions with domain wall fermions
• Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions
• Chiral properties of domain-wall fermions from eigenvalues of 4 dimensional Wilson-Dirac operator
• The overlap operator as a continued fraction
• Considerations on Neuberger's operator
• A comparative study of numerical methods for the overlap Dirac operator--a status report
• Overlap Fermions on a $20^4$ Lattice
• A Study of the 't Hooft Model with the Overlap Dirac Operator
• Chiral Fermions and Multigrid
• The Tunneling Hybrid Monte-Carlo algorithm
• A numerical solution to the local cohomology problem in U(1) chiral gauge theories
• Hadron Masses and Quark Condensate from Overlap Fermions
• Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
• Speed and Adaptability of Overlap Fermion Algorithms
• Bound states for Overlap and Fixed Point Actions close to the chiral limit
• Combining the color structures and intersection points of thick center vortices and low-lying Dirac modes
• Lattice QCD and the Neutron Electric Dipole Moment
• Differential equation for spectral flows of hermitean Wilson-Dirac operator
• Feasibility study of using the overlap-Dirac operator for hadron spectroscopy
• Generalised Spin Projection for Fermion Actions
• Improving the low-lying spectrum of the overlap kernel
• FLIC-Overlap Fermions and Topology
• Probing the QCD vacuum with overlap fermions
• Fractional topological charges and the lowest Dirac modes
• Index theorem with Minimally Doubled Fermions in four space-time dimensions
• Overlap Dirac Operator, Eigenvalues and Random Matrix Theory
• Zero-modes of the QED Neuberger Dirac operator
• FLIC Overlap Fermions