The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes

Understand

We present numerical results for the Rosenzweig Porter model for all symmetry classes of the Dyson threefold way.

• We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results.
• Based on these results we propose characteristics of the spectral properties as measures to explore the transition from Poisson to Wigner Dyson WD statistics.
• Furthermore, we performed thorough studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback Leibler KL divergences and the fidelity susceptibility.