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

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Abstract
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. DOI: http://dx.doi.org/10.1103/PhysRevB.41.888 © 1990 The American Physical Society