Universal spectral correlations at the mobility edge

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Authors

Colleges, School and Institutes

Abstract

We demonstrate the level statistics in the vicinity of the Anderson transition in d > 2 dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels N in a given energy interval with [N] >> 1 is proved to behave as (N)gamma where gamma = 1 - (nud)-1 and nu is the correlation length exponent. The inequality gamma <1, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.

Details

Original languageEnglish
Pages (from-to)888-891
Number of pages4
JournalPhysical Review Letters
Volume72
Issue number6
Publication statusPublished - 1 Feb 1994