Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-05-27
Physical Review B 66, 195113 (2002)
Physics
Condensed Matter
Disordered Systems and Neural Networks
RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published)
Scientific paper
10.1103/PhysRevB.66.195113
We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $ L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .
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