Level curvature distribution and the structure of eigenfunctions in disordered systems

Abstract

The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric s model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for T-breaking perturbations caused by a constant vectorpotential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasilocalized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In two-dimensional (2D) systems the distribution function P(K) has a branching point at K=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent d2 is suggested. Evidence of the branch-cut singularity is found in numerical simulations in 2D systems and at the Anderson transition point in 3D systems.

Publication DOI: https://doi.org/10.1103/PhysRevB.57.14174
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: ©1998 American Physical Society
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Related URLs: http://journals ... ysRevB.57.14174 (Publisher URL)
PURE Output Type: Article
Published Date: 1998-06-01
Authors: Basu, C.
Canali, C.M.
Kravtsov, V.E.
Yurkevich, I.V. ( 0000-0003-1447-8913)

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