behavior of the DOS at higher $t_\perp= 0.8$ displays a rather simple evolution. As shown by the data in the B/AB basis (dotted blue and dot-dashed orange) we observe that the total DOS (thick black) is the average of the two semicircular contributions of the B and AB bands. The gap opens continuously and the effective masses or, equivalently, the bandwidth of the two bands remains essentially un-renormalized. The insulator at $U>U_{c_3}$ is clearly a band insulator state. As we mentioned before, we identify this state with the Peierls insulator, since it is realized at large $t_\perp$ and relatively low $U$. We may also note that at the highest values of the interaction $U$ this simple description begins to fail as the B and AB DOS begin to develop a second contribution to the spectral weight for $\omega$ &gt; 0 and &lt; 0, respectively. We shall discuss this feature in more detail latter on.

In contrast, the transition at lower values of $t_\perp= 0.3$ is significantly different. The evolution of the DOS is more complex and has various contributions. We can immediately observe the strongly correlated (Mott-Hubbard) character by noticing a characteristic 3-peak structure at intermediate values of the interaction. 