Critical parameters from generalised multifractal analysis at the Anderson transition

Alberto Rodriguez; Louella J. Vasquez; Keith Slevin; Rudolf A. Römer

doi:10.1103/physrevlett.105.046403

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arXiv · 1005.0515

Critical parameters from generalised multifractal analysis at the Anderson transition

Alberto Rodriguez·Louella J. Vasquez·Keith Slevin·Rudolf A. Römer

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Abstract

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent $ν=1.58\pm 0.03$.

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Alberto Rodriguez, Louella J. Vasquez, Keith Slevin, Rudolf A. Römer. 2010-05-04. Critical parameters from generalised multifractal analysis at the Anderson transition. https://doi.org/10.1103/physrevlett.105.046403

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