Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition

Abstract

The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as the system size is varied exactly at a value obtained from the scaling properties of the typical value of the inverse participation number. Therefore the state-to-state fluctuation of the correlation dimension is tightly linked to the scaling properties of the joint probability distribution of the eigenstates.

4 pages, 5 figures

References in corpus (2)

• Dimensionality dependence of the wave function statistics at the Anderson transition
• Fluctuations of the correlation dimension at metal-insulator transitions

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