$f(\alpha )$ Multifractal spectrum at strong and weak disorder

Abstract

The system size dependence of the multifractal spectrum $f(\alpha )$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that $f(\alpha )$ is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, $f(\alpha )$ strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength.

RevTex4, 6 two-column pages, 4 .eps figures, new results added, updated references, to be published in Phys. Rev. B

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• Anderson transition in systems with chiral symmetry
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• Criticality in the Quantum Kicked Rotor with a Smooth Potential
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
• Two-level correlation function of critical random-matrix ensembles
• Critical properties in long-range hopping Hamiltonians
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• Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields
• Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry
• Effect of spin-orbit coupling in one-dimensional quasicrystals with power-law hopping
• Statistical properties of two-particle transmission at Anderson transition