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Correlated random band matrices: localization-delocalization transitions

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  • 1Institut fur Theoretische Physik III, Ruhr-Universitat Bochum, 44780 Bochum, Germany.


We study the statistics of eigenvectors in correlated random band matrix models. These models are characterized by two parameters, the bandwidth B(N) of a Hermitian NxN 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) approximately sqrt[N] and C(N) approximately sqrt[N], the model shows a localization-delocalization transition of the quantum Hall type.

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