Localization properties of lattice fermions with plaquette and improved gauge actions

We determine the location $\lambda_c$ of the mobility edge in the spectrum of the hermitian Wilson operator in pure-gauge ensembles with plaquette, Iwasaki, and DBW2 gauge actions. The results allow mapping a portion of the (quenched) Aoki phase diagram. We use Green function techniques to study the localized and extended modes. Where $\lambda_c>0$ we characterize the localized modes in terms of an average support length and an average localization length, the latter determined from the asymptotic decay rate of the mode density. We argue that, since the overlap operator is commonly constructed from the Wilson operator, its range is set by the value of $\lambda_c^{-1}$ for the Wilson operator. It follows from our numerical results that overlap simulations carried out with a cutoff of 1 GeV, even with improved gauge actions, could be afflicted by unphysical degrees of freedom as light as 250 MeV.