and consequently $n_f>1$ and the relevant carriers are hybrid in nature. However, the $f$- and $p$-character of the model solution can still be used to indicate the projection onto the correlated and non-correlated orbital respectively. Upon increasing the interaction strength (see central panel of ) we first observe the formation of a correlated metallic state. This is characterized by the presence in the density of states (DOS) of a metallic feature at the Fermi level, flanked by the two precursors of the Hubbard bands. A Mott insulating state is then obtained further increasing the correlation $U$. The system opens a spectral gap at the Fermi energy (see bottom panel of ) with a width controlled by the correlation $U$.[@sordi09] To fix ideas, in the remaining part of this work we shall set the correlation and the hybridization to, respectively, $U=2.0$ and $\tpd=0.9$. This choice of the model parameters corresponds to a Mott insulating state for $n_\mathrm{tot}=3$. Similar results can be obtained for different values of correlation and hybridization.

The Mott insulator can be destabilized in favor of a correlated metallic phase by either adding or removing electrons (creating holes). As first noticed in Ref.  the two transitions have a different 