The square root of the positive definite hermitian operator Dw†Dw in Neuberger's proposal of exactly massless quarks on the lattice is
implemented by the recursion formula Yk+1=1/2(Yk+Dw†DwYk−1) with Y_0 = \Id, where Yk2 converges to Dw†Dw
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.Comment: 18 pages (LaTeX), 2 figures (EPS