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In recent years it became clear that the metallic regime of systems thatexhibit a many body localization (MBL) behavior show properties which are quitedifferent than the vanilla metallic region of the single particle Andersonregime. Here we show that the large scale energy spectrum of a canonicalmicroscopical model featuring MBL, displays a non-universal behavior atintermediate scales, which is distinct from the deviation from universalityseen in the single particle Anderson regime. The crucial step in revealing thisbehavior is a global unfolding of the spectrum performed using the singularvalue decomposition (SVD) which takes into account the sample to samplefluctuations of the spectra. The spectrum properties may be observed directlyin the singular value amplitudes via the scree plot, or by using the SVD tounfold the spectra and then perform a number of states variance calculation.Both methods reveal an intermediate scale of energies which follow superPosissonian statistics.

Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields