Distribution of level curvatures for the Anderson model at the localization-delocalization transition

C. M. Canali; Chaitali Basu; W. Stephan; V. E. Kravtsov

doi:10.1103/physrevb.54.1431

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Distribution of level curvatures for the Anderson model at the localization-delocalization transition

C. M. Canali·Chaitali Basu·W. Stephan·V. E. Kravtsov

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Abstract

We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators $P(k)$ has a logarithmically-normal form. At the Anderson localization-delocalization transition $P(k)$ fits very well the proposed novel distribution $P(k)\propto (1+k^μ)^{3/μ}$ with $μ\approx 1.58$, which approaches the RMT result for large $k$ and is non-analytical at small $k$. We ascribe such a non-analiticity to the spatial multifractality of the critical wave functions.

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C. M. Canali, Chaitali Basu, W. Stephan, V. E. Kravtsov. 1996-02-05. Distribution of level curvatures for the Anderson model at the localization-delocalization transition. https://doi.org/10.1103/physrevb.54.1431

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