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The effect of doping on the TB model of the CuO planes in the La2CuO4constructed in previous works is investigated. Firstly, it is noted that themodel employed constitutes a generalization of the Hubbard one for the samesystem. Thus, the former predictions of the insulator gap, antiferromagneticcharacter and the existence of a paramagnetic-pseudogap state, become naturalones to be expected from this more general picture. The effect of hole dopingon the antiferromagnetic-insulator state (AFI) and the paramagnetic-pseudogapone, is investigated. The results predict a quantum phase transition (QPT) fromthe AFI state at low doping to a paramagnetic-metallic state (PM) at higherhole densities. Therefore, a clear description of the hidden QPT laying beneaththe dome in high critical temperature superconducting materials is found. Atlow doping, the system prefers the AFI state, and at the critical value of thedoping density 0.2, the energy of a metallic state becomes lower. The evolutionwith small doping values of the band spectrum of the AFI state, shows that theholes tend to become localized at the middle of the sides of the reducedBrillouin zone (BZ). Then, around the critical value, the holes of the AFIstate move to become situated at the corners of the same reduced BZ, showing astructural change at the phase transition point. Thus, the PM state appearingat the QPT acquires the same behavior with respect to the position of holes asthe pseudogap state. In the small doping limit a clear difference between thedegree of convergence of the iterative self-consistent solution is associatedto an even or odd number of electrons. It suggests that the Kramersdegeneration in combination with the spin-spatial entangled nature of the holestates, leads to a new kind of pair interaction between two holes. The bindingenergy value is estimated as a function of the screening.

Quantum phase transition from a Antiferromagnetic-Insulator to a Paramagnetic-Metal laying beneath the superconducting dome