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

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

1998-04-13

arxiv.org/abs/hep-lat/9804016v4

Phys.Rev.D58:074511,1998

Physics

High Energy Physics

High Energy Physics - Lattice

18 pages (LaTeX), 2 figures (EPS)

Scientific paper

10.1103/PhysRevD.58.074511

The square root of the positive definite hermitian operator $D_w^{\dagger} D_w$ in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula $Y_{k+1} = {1/2} (Y_k + D_w^{\dagger} D_w Y_k^{-1})$ with $Y_0 = \Id$, where $Y_k^2$ converges to $D_w^{\dagger} D_w$ 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.

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