Comparing lattice Dirac operators in smooth instanton backgrounds

We compare the behavior of different lattice Dirac operators in gauge backgrounds which are lattice discretizations of a classical instanton. In particular, we analyze the standard Wilson operator, a chirally improved Dirac operator and the overlap operators constructed from these two operators. We discuss the flow of real eigenvalues as a function of the instanton size. An analysis of the eigenvectors shows that overlap fermions with the Wilson operator as input operator have difficulties with reproducing the continuum zero mode already for moderately small instantons. This problem is greatly reduced when using the chirally improved operator for the overlap projection.