We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Lambda(QCD) while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. The situation changes drastically when we study "vortex removed" configurations.
@article{arxiv.hep-lat/0510098,
title = {Localization of Low Lying Eigenmodes for Chirally Symmetric Dirac Operator},
author = {M. I. Polikarpov and F. V. Gubarev and S. M. Morozov and V. I. Zakharov},
journal= {arXiv preprint arXiv:hep-lat/0510098},
year = {2007}
}