Self-consistent theory of Anderson localization for the tight-binding model with site-diagonal disorder

We present a self-consistent theory of the frequency-dependent conductivity with no adjustable parameters for a tight-binding model with random energy levels, using the locator expansion. The resulting phase diagram and the conductivity and localization length as a function of energy and disorder are in quantitative agreement with results of numerical diagonalization of finite-size systems. The results demonstrate for the first time that quantum interference effects are responsible for localization over the complete energy range, including the band edges.