Large-N expansion based on the Hubbard operator path integral representation and its application to the t-J model.: II.: The case for finite J -: art. no. 205123

We have introduced a new perturbative approach for t-J-V model where Hubbard operators are treated as fundamental objects. Using our vertices and propagators we have developed a controllable large-N expansion to calculate different correlation functions. We have investigated charge density-density response and the phase diagram of the model. The charge correlations functions are not very sensitive to the value of J and they show collective peaks (or zero sound) which are more pronounced when they are well separated (in energy) from the particle-hole continuum. For a given J a Fermi liquid state is found to be stable for doping delta larger than a critical doping delta(c). delta(c) decreases with decreasing J. For the physical region of the parameters and, for delta<delta(c), the system enters in an incommensurate flux or DDW phase. The inclusion of the nearest-neighbor Coulomb repulsion V leads to a charge density wave phase when V is larger than a critical value V-c. The dependence of V-c with delta and J is shown. We have compared the results with other ones in the literature.