A mean-field theory of Anderson localization

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.

REVTeX4, 4 pages, 2 EPS figures

Cited by in corpus (12)

• One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Self-Consistent Theory of Anderson Localization: General Formalism and Applications
• Localization of eigenvectors in random graphs
• Mean-field theories for disordered electrons: Diffusion pole and Anderson localization
• Fate of localization in coupled free chain and disordered chain
• Localization in random bipartite graphs: numerical and empirical study
• Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Vertex corrections to the mean-field electrical conductivity in strongly disordered electron systems
• Quantum diffusion in a random potential: A consistent perturbation theory