Lattice instantons, a basis for a treatment of localized states?

Abstract

We consider instanton-type solutions for a lattice model of the disordered electronic system where both the diagonal and the offdiagonal matrix elements are taken as Gaussian distributed random variables. For a large range of distributions we show that the dominant instanton solution is localized at a single site. This solution is taken as the starting point for a perturbation expansion in powers of 1/E2 in the region of localized states. This expansion has many features in common with the well-known high-temperature expansions, and we suggest to use it for an estimate of critical exponents. We evaluate the first few terms in the expansions of the density of states, the participation ratio, and the localization length for the case of nearest-neighbour hopping on a simpled-dimensional lattice. The tendency of the numerical results is promising.