Correlated random band matrices: Localization-delocalization transitions

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) similar to root N and C(N) similar to root N, the model shows a localization-delocalization transition of the quantum Hall type.