  In recent years it became clear that the metallic regime of systems that
exhibit a many body localization (MBL) behavior show properties which are quite
different than the vanilla metallic region of the single particle Anderson
regime. Here we show that the large scale energy spectrum of a canonical
microscopical model featuring MBL, displays a non-universal behavior at
intermediate scales, which is distinct from the deviation from universality
seen in the single particle Anderson regime. The crucial step in revealing this
behavior is a global unfolding of the spectrum performed using the singular
value decomposition (SVD) which takes into account the sample to sample
fluctuations of the spectra. The spectrum properties may be observed directly
in the singular value amplitudes via the scree plot, or by using the SVD to
unfold the spectra and then perform a number of states variance calculation.
Both methods reveal an intermediate scale of energies which follow super
Posissonian statistics.
