Energy level statistics at the metal-insulator transition in the Anderson model of localization with anisotropic hopping
Abstract
Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders Wc have been obtained within the accuracy of the data. We now employ energy level statistics (ELS) to further characterize the MIT. We find a crossover of the nearest-neighbor level spacing distribution P(s) from GOE statistics at small disorder indicating metallic behavior to the Poisson distribution at large disorder characteristic for localized states. An analysis of the system size dependence of the spectral rigidity 3(L) confirms the values of Wc from TMM and MFA.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.