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A mean-field theory of Anderson localization

V. Janis·J. Kolorenc
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Abstract

Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this simplification and with the electron-hole symmetry we reduce the parquet equations for two-particle irreducible vertices to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signalling vanishing of diffusion and onset of Anderson localization. There is no bifurcation in $d=1,2$ where all states are localized. A natural order parameter for Anderson localization pops up in the construction.

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V. Janis, J. Kolorenc. 2004-02-18. A mean-field theory of Anderson localization. https://doi.org/10.1103/physrevb.71.033103

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