Correlated random band matrices: localization-delocalization transitions

Abstract

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.

12 pages, 11 postscript figures

References in corpus (3)

• Statistics of energy levels and eigenfunctions in disordered systems
• Distribution of fractal dimensions at the Anderson transition
• Realistic model of correlated disorder and Anderson localization

Cited by in corpus (9)

• Localization in the quantum Hall regime
• Topological invariant in three-dimensional band insulators with disorder
• Anomalously localized states and multifractal correlations of critical wavefunctions in two-dimensional electron systems with spin-orbital interactions
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Spectral form factor and energy correlations in banded random matrices
• A new strategy for directly calculating the minimum eigenvector of matrices without diagonalization
• Establishing simple relationship between eigenvector and matrix elements
• Level-spacing distribution of a fractal matrix
• Electronic localization in two dimensions