How the Mott and pseudogap states coalesce beneath the superconductor Dome

Former results of a Tight-Binding (TB) model of CuO planes in La$_{\mathrm{2}}$CuO$_{\mathrm{4}}$ are reviewed to underline their wider implications. It is noted that physical systems being appropriately described by the TB model can exhibit the main strongly correlated electron system (SCES) properties, when they are solved in the HF approximation, by also allowing crystal symmetry breaking effects and non-collinear spin orientations of the HF orbitals. In particular, it is argued how a simple 2D square lattice system of Coulomb interacting electrons can exhibit insulator gaps and pseudogap states, and quantum phase transitions as illustrated by the mentioned former works. These results allow to understand the nature of the observed quantum phase transition laying ``beneath'' the superconducting Dome. It corresponds to coalescence under hole doping increase, of an insulator ground state (with a highly degenerated spin order) with an excited pseudogap state, showing a lattice order symmetry breaking. The evolution of the band structure and Fermi surface with doping are determined.