Real-space rescaling method for disordered systems

Abstract

An exact real-space rescaling approach for disordered tight-binding model Hamiltonians is presented. The method provides a direct way of obtaining the local Green's functions and the local density of states. The behavior of the eigenstates in a given region of energy can be determined from the behavior of the rescaling transformation under iteration. Localized-mode behavior is characterized by a fixed point of the transformation and the inverse localization length can be obtained directly from an analysis of the approach to this fixed point. The problem of a single impurity is studied in detail and our method is compared with the standard treatment of such problems.