Localized eigenstates of one-dimensional tight-binding systems: A new algorithm

Abstract

We present a new numerical algorithm capable of determining the localized eigenstates and their energies for the general class of one-dimensional nearest-neighbor tight-binding models to arbitrarily high accuracy. This algorithm completely overcomes the numerical instability originating in a growing solution which inevitably accompanies a localized solution. It is also free of the ambiguity of the Economou-Cohen method.