Correlated random band matrices: localization-delocalization transitions

Details Correlated random band matrices: localization-delocalization transitions Correlated random band matrices: localization-delocalization transitions

1999-11-29

arxiv.org/abs/cond-mat/9911467v1

Phys. Rev. E, 61 (2000) 6278

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 11 postscript figures

Scientific paper

10.1103/PhysRevE.61.6278

We study the statistics of eigenvectors in correlated random band matrix models. These models are characterized by two parameters, the band width B(N) of a Hermitian N times N matrix and the correlation parameter C(N) describing correlations of matrix elements along diagonal lines. The correlated band matrices show a much richer phenomenology than models without correlation as soon as the correlation parameter scales sufficiently fast with matrix size. In particular, for B(N) and C(N) increasing like the square root of N the model shows a localization-delocalization transition of the quantum Hall type.

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