Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime
Department of Physics and Centre for Computational Science and
Engineering, National University of Singapore, 117542
Singapore, Republic of
2 NUS Graduate School for Integrative Sciences and Engineering, 117597 Singapore, Republic of Singapore
Present address: Department of Physics, Birla Institute of Technology and
Science, 333031 Pilani, India.
b e-mail: firstname.lastname@example.org
Received in final form: 21 August 2012
Published online: 1 October 2012
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012