Scaling properties near the Anderson transition

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Abstract
We present detailed results of analytical and numerical investigations of the Anderson metal-insulator (MI) transition based on a supersymmetric nonlinear σ model in the effective-medium approximation. We show that in the critical metallic regime the density-of-states correlation function has two characteristic length scales ξ and ζ which diverge according to a power law but have different critical exponents. Moreover, we derive that the level broadening depends exponentially on the shorter length ζ and put forward a physical interpretation that enables us to express the diffusion coefficient in terms of these two lengths. We argue that in the vicinity of the MI transition the properties of the system are determined by the correlation length ζ, which is related to the typical size of classically forbidden regions, and the phase-coherence length, which sets the scale for self-averaging of the density-of-states correlator. Relating the level broadening due to tunneling along a distance ξ and the Thouless length, we reproduce earlier results on the critical exponential behavior of the diffusion coefficient.