Abstract: The effect of hole doping on the Tight-Binding (TB) model of the Cu-O planes in the La2CuO4 constructed in previous works is investigated here. Firstly, it is pointed out that the model employed constitutes a generalization of the Hubbard one for the same system. Thus, the former predictions of the insulator gap, antiferromagnetic (AF) character and the existence of a paramagnetic-pseudogap (PPG) state at half-filling, become natural ones to be expected from this more general picture. The effect of hole doping on the antiferromagnetic-insulator state (AFI) and the paramagnetic-pseudogap one at half-filling, is investigated here at T = 0 K. The results predict the occurrence of a quantum phase transition (QPT) from the antiferromagnetic- insulator state at low doping to a paramagnetic-metallic state (PM) at higher hole densities. Therefore, a clear description of the hidden QPT laying beneath the “dome” in high critical temperature (HTc) superconducting materials is found. At low doping, the systems prefers the AFI state, and at the critical value of the doping density dc = 0.2, the energy of a metallic state starts becoming lower. The evolution with small doping values of the band spectrum of the AFI state, shows that the holes tend to become localized at the middle of the sides of the reduced Brillouin zone (BZ). Then, when passes through the critical value, the holes of the AFI state move to become situated at the corners of the same reduced BZ, showing in this way a structural change at the phase transition point. It suggests that the Kramers degeneration in combination with the spin-spatial entangled nature of the hole states, can lead to a new kind of pair interaction between two holes. The binding energy value is estimated as a function of the screening.