The central peak, which gives the metallic character becomes narrower as it losses spectral weight that is transferred to build the high energy Hubbard bands at energy of order $\pm U/2$. Interestingly and contrary to the single band Hubbard model case, there is no pinning condition for the central quasiparticle peak [@moeller1999_rkky_interactions_mott_transition] and this quasiparticle develops a non-trivial structure in the DOS at low frequencies as the critical value $U_{c_2}$ is approached. We shall come back to this point also later on. Unlike the higher $t_\perp$ case, the decomposition of the DOS in the B/AB contributions do not seem to provide any simpler picture of the evolution.

We can gain further insight on this transition by tracking the behavior of the self-energy through the two parameters that we defined above for the R2B model, $Z$ and $\eta$, that we show in Fig. \[fig:transition\_orderparam\].

![$Z$ and $| \eta |$ as a function of $U$ for various values of dimerization $t_\perp$. The left and central panels correspond to the behavior as the $U_{c_2}(t_\perp)$ red spinodal line is approached (cf. Fig.\[fig:phasediag\]), where the metal-insulator transition is discontinuous. The right panel shows the behavior when the green 2$^{\text{nd}}$ order line is crossed (cf. Fig.\[fig:phasediag\]). 