Self-consistent scaling theory of the metal-insulator transition in disordered systems

We propose a self-consistent description of the diffusion of electrons dressed by the Coulomb exchange interactions in a disordered system, as the metal-insulator transition is approached from the metallic side. The critical anomalies of the single-particle density of states and dielectric function are evaluated each in terms of the other. New scaling laws between the critical behaviors of these quantities as well as the diffusion constant and the frequency-dependent conductivity are obtained. It is argued that the density of states which appears in the expressions for the conductivity and the dielectric function becomes the anomalous one for frequencies higher than some relaxation rate of the many-body system. © 1983 The American Physical Society.