Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice

Abstract

The square root of the positive definite hermitian operator $D_w^{†}{D}_w$ in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula $Y_{k+1}=1/2(Y_k+D_w^{†}{D}_w{Y}_k^{-1})$ with $Y_0 = \Id$, where $Y_k^2$ converges to $D_w^{†}{D}_w$ quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investigated. For smooth background gauge fields with non-zero topological charge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the Index Theorem is satisfied exactly. The fermionic determinants are also computed and they are in good agreement with the continuum exact solution.

18 pages (LaTeX), 2 figures (EPS)

References in corpus (14)

• 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
• Domain wall quarks and kaon weak matrix elements
• Overlap in odd dimensions
• Ginsparg-Wilson relation and the overlap formula
• A numerical test of the continuum index theorem on the lattice
• Consistent and covriant anomalies in the overlap formulation of chiral gauge theories
• The theoretical background and properties of perfect actions
• Fractional Inversion in Krylov Space
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
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Cited by in corpus (53)

• Locality properties of Neuberger's lattice Dirac operator
• A practical implementation of the Overlap-Dirac operator
• Solutions of the Ginsparg-Wilson Relation
• Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator
• Lattice QCD with Ginsparg-Wilson fermions
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• Axial vector current of exact chiral symmetry on the lattice
• Algebraic Generalization of the Ginsparg-Wilson Relation
• On the continuum limit of fermionic topological charge in lattice gauge theory
• The axial anomaly of Ginsparg-Wilson fermion
• Minimizing storage in implementations of the overlap lattice-Dirac operator
• Exact Pseudofermion Action for Monte Carlo Simulation of Domain-Wall Fermion
• Relation $Tr{\gamma }_5=0$ and the index theorem in lattice gauge theory
• Ginsparg-Wilson operators and a no-go theorem
• CP breaking in lattice chiral gauge theories
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• The Index of a Ginsparg-Wilson Dirac operator
• Some remarks on the Ginsparg-Wilson fermion
• Chiral Anomaly for a New Class of Lattice Dirac Operators
• Topological Phases in Neuberger-Dirac operator
• Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
• More chiral operators on the lattice
• Ginsparg-Wilson Fermions: A study in the Schwinger Model
• Numerical study of lattice index theorem usingimproved cooling and overlap fermions
• Fermions on tori in uniform abelian fields
• Fermion determinant for general background gauge fields
• Domain-Wall Fermion with $R_5$ Symmetry
• Topological susceptibility in finite temperature QCD with physical $(u/d,s,c)$ domain-wall quarks
• Domain wall fermion and CP symmetry breaking
• Quenched chiral logarithms in lattice QCD with exact chiral symmetry
• Characteristics of Chiral Anomaly in View of Various Applications
• A note on the solutions of the Ginsparg-Wilson relation
• Majorana and Majorana-Weyl fermions in lattice gauge theory
• Quantum anomalies and some recent developments
• Can nonlocal Dirac operators be topologically proper ?
• Chiral fermions on the lattice and index relations
• Bound states for Overlap and Fixed Point Actions close to the chiral limit
• Form and index of Ginsparg-Wilson fermions
• Speed and Adaptability of Overlap Fermion Algorithms
• General chiral gauge theories on the lattice
• Factorization of Fermion Doubles on the Lattice
• Absence of strong CP violation
• Berry's phase and chiral anomalies
• The Index and Axial Anomaly of a lattice Dirac operator
• Chiral fermion operators on the lattice
• Exactly massless fermions on the lattice
• Naive Lattice Fermion without Doublers
• Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture
• Repercussions of the Peccei-Quinn axion on QCD
• Topologically invariant transformation for lattice fermions
• Topological Obstruction in Block-spin Transformations
• Criterium for the index theorem on the lattice
• More chiral lattice fermions