Multifractal Analysis of the Metal-insulator Transition in Anisotropic Systems Preprint-reihe Des Chemnitzer Sfb 393 Multifractal Analysis of the Metal-insulator Transition in Anisotropic Systems
نویسندگان
چکیده
We study the Anderson model of localization with anisotropic hopping in three dimensions for weakly coupled chains and weakly coupled planes. The eigenstates of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes up to 48 3 , show multifractal behavior at the metal-insulator transition even for strong anisotropy. The critical disorder strength W c determined from the system size dependence of the singularity spectra is in a reasonable agreement with a recent study using transfer matrix methods. But the respective spectrum at W c deviates from the \characteristic spec-trum" determined for the isotropic system. This indicates a quantitative diierence of the multifractal properties of states of the anisotropic as compared to the isotropic system. Further, we calculate the Kubo conductivity for given anisotropies by exact diagonalization. Already for small system sizes of only 12 3 sites we observe a rapidly decreasing conductivity in the directions with reduced hopping if the coupling becomes weaker.
منابع مشابه
Numerische Simulation Auf Massiv Parallelen Rechnern Energy Level Statistics at the Metal-insulator Transition in the Anderson Model of Localization with Anisotropic Hopping Preprint-reihe Des Chemnitzer Sfb 393
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