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

Ting-Wai Chiu
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Abstract

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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Ting-Wai Chiu. 1998-06-12. Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice. https://doi.org/10.1103/physrevd.58.074511

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