  The Rosenzweig-Porter model has seen a resurgence in interest as it exhibits
a non-ergodic extended phase between the ergodic extended metallic phase and
the localized phase. Such a phase is relevant to many physical models from the
Sachdev-Ye-Kitaev model in high-energy physics and quantum gravity, to the
interacting many-body localization in condensed matter physics and quantum
computing. This phase is characterized by fractal behavior of the
wavefunctions, and a postulated correlated mini-band structure of the energy
spectrum. Here we will seek evidence for the latter in the spectrum. Since this
behavior is expected on intermediate energy scales spectral rigidity is a
natural way to tease it out. Nevertheless, due to the Thouless energy and
ambiguities in the unfolding procedure, the results are inconclusive. On the
other hand, by using the singular value decomposition method, clear evidence
for a super-Poissonian behavior in this regime emerges, consistent with a
picture of correlated mini-bands.
