2004/02/18 by V. Janiš, V. Janis, J. Kolorenc +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Anderson impurity model #Anderson localization #Bifurcation #Bifurcation theory #Combinatorics #Diagonal #Electron #Gaussian #Geometry #Magnetic properties of thin films #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear system #Physics #Propagator #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Symmetry (geometry) #Vertex (graph theory) #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.71.033103
published as Phys. Rev. B71, 033103 (2005) · REVTeX4, 4 pages, 2 EPS figures
arxiv created 2004/02/18 · openalex publication_date 2005/01/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The 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 with respect to 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 signaling 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 emerges from the construction.