Ginsparg-Wilson Fermions: A study in the Schwinger Model

Abstract

Qualitative features of Ginsparg-Wilson fermions, as formulated by Neuberger, coupled to two dimensional U(1) gauge theory are studied. The role of the Wilson mass parameter in changing the number of massless flavors in the theory and its connection with the index of the Dirac operator is studied. Although the index of the Dirac operator is not related to the geometric definition of the topological charge for strong couplings, the two start to agree as soon as one goes to moderately weak couplings. This produces the desired singularity in the quenched chiral condensate which appears to be very difficult to reproduce with staggered fermions. The fermion determinant removes the singularity and reproduces the known chiral condensate and the meson mass within understandable errors.

Corrected a few typos and changed some references. Minor changes to the content

References in corpus (18)

• 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
• Vector like gauge theories with almost massless fermions on the lattice
• Lattice QCD without tuning, mixing and current renormalization
• Prospects for perfect actions
• Spectral flow, condensate and topology in lattice QCD
• Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions
• Ginsparg-Wilson Relation and Ultralocality
• Domain wall quarks and kaon weak matrix elements
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• A numerical test of the continuum index theorem on the lattice
• Monte Carlo evaluation of a fermion number violating observable in 2D
• Reducing Chiral Symmetry Violations in Lattice QCD with Domain-Wall Fermions
• Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
• Chiral properties of the fixed point action of the Schwinger model
• Domain wall fermion zero modes on classical topological backgrounds
• The overlap passes a chiral dynamical test in two dimensions

Cited by in corpus (14)

• Scaling tests with dynamical overlap and rooted staggered fermions
• Staggered versus overlap fermions: a study in the Schwinger model with $N_f=0,1,2$
• The construction of generalized Dirac operators on the lattice
• Theta vacuum effects on the chiral condensation and the eta^prime meson correlators in the two-flavor massive QED_2 on the lattice
• Schwinger Model with the Overlap-Dirac Operator: exact results versus a physics motivated approximation
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Topological Phases in Neuberger-Dirac operator
• General bounds on the Wilson-Dirac operator
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• A Study of the 't Hooft Model with the Overlap Dirac Operator
• Divergent chiral condensate in the quenched Schwinger model
• Gross-Neveu model with overlap fermions
• Pion mass and the PCAC relation in the overlap fermion formalism: Gauged Gross-Neveu model on a lattice
• Criterium for the index theorem on the lattice