Doping-dependent evolution of low-energy excitations and quantum phase transitions within effective model for High-Tc copper oxides

In this paper a mean-field theory for the spin-liquid paramagnetic non-superconducting phase of the p- and n-type High-$T_c$ cuprates is developed. This theory applied to the effective $t-t'-t''-J^*$ model with the {\it ab initio} calculated parameters and with the three-site correlated hoppings. The static spin-spin and kinematic correlation functions beyond Hubbard-I approximation are calculated self-consistently. The evolution of the Fermi surface and band dispersion is obtained for the wide range of doping concentrations $x$. For p-type systems the three different types of behavior are found and the transitions between these types are accompanied by the changes in the Fermi surface topology. Thus a quantum phase transitions take place at $x=0.15$ and at $x=0.23$. Due to the different Fermi surface topology we found for n-type cuprates only one quantum critical concentration, $x=0.2$. The calculated doping dependence of the nodal Fermi velocity and the effective mass are in good agreement with the experimental data.