next subsections.

![The Metal-Insulator transition takes place along the $U_{c_1}$, $U_{c_2}$ and $U_{c_3}$ lines (blue, red and green respectively). The $U_{c_2}$ line corresponds to a spinodal line where the metallic solution discontinuously disappears upon increasing $U$. Along the $U_{c_3}$ line there is a continuous 2nd order metal-insulator transition. The $U_{c_1}$ line marks the spinodal where the Mott insulator vanishes discontinuously upon decreasing $U$. The Mott insulator is continuously connected to the Peierls insulator, however different crossover behaviors can be identified. \[fig:phasediag\]](phasediagram.pdf){width="\linewidth"}

Metal to insulator transitions across $U_{c_2}$ and $U_{c_3}$ {#sec:org1c3ef86}
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The metal to insulator transition by increasing $U$ dramatically changes its character as a function of $t_\perp$. In Fig. \[fig:dimer\_transition\_spectra\] we illustrate this by showing the evolution of the frequency-dependent DOS with increasing $U$, for two representative values $t_\perp=0.3$ and 0.8, that respectively cross the $U_{c_2}$ and the $U_{c_3}$ lines.

![DOS for increasing values of $U$ crossing the red $U_{c_1}$ and the green $U_{c_3}$ boundary lines (left and right panels, respectively) of the phase diagram of Fig. \[fig:phasediag\]. Black lines represent the local($-\Im m G_{11}$) Spectral function, which is the average of the bonding (dashed blue) and anti-bonding (dot dashed orange) bands, calculated at $T=0$ with IPT. \[fig:dimer\_transition\_spectra\]](dimer_transition_spectra.pdf){width="\linewidth"}

The 