Power-law random banded unitary matrices (PRBUM), whose matrix elements decay
in a power-law fashion, were recently proposed to model the critical statistics
of the Floquet eigenstates of periodically driven quantum systems. In this
work, we numerically study in detail the statistical properties of PRBUM
ensembles in the delocalization-localization transition regime. In particular,
implications of the delocalization-localization transition for the fractal
dimension of the eigenvectors, for the distribution function of the eigenvector
components, and for the nearest neighbor spacing statistics of the eigenphases
are examined. On the one hand, our results further indicate that a PRBUM
ensemble can serve as a unitary analog of the power-law random Hermitian matrix
model for Anderson transition. On the other hand, some statistical features
unseen before are found from PRBUM. For example, the dependence of the fractal
dimension of the eigenvectors of PRBUM upon one ensemble parameter displays
features that are quite different from that for the power-law random Hermitian
matrix model. Furthermore, in the time-reversal symmetric case the nearest
neighbor spacing distribution of PRBUM eigenphases is found to obey a
semi-Poisson distribution for a broad range, but display an anomalous level
repulsion in the absence of time-reversal symmetry.Comment: 10 pages + 13 fig
