Large-Nexpansion based on the Hubbard operator path integral representation and its application to thet−Jmodel. II. The case for finite

A. Foussats

¹

,

A. Greco

²

Abstract

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 densitydensity 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 δ larger than a critical doping δc. δc decreases with decreasing J. For the physical region of the parameters and, for δ < δc, the system enters in an incommensurate flux or DDW phase. The inclusion of the nearest-neighbors Coulomb repulsion V leads to a CDW phase when V is larger than a critical value Vc. The dependence of Vc with δ and J is shown. We have compared the results with other ones in the literature.

Self-energy effects in cuprates and the dome-shaped behavior of the superconducting critical temperature

“…The path integral large-N approach for the t-J model in the context of Hubbard operators, 31 allows the computation of fluctuations above the mean-field level and the calculation of self-energy effects.…”

“…The instability of the paramagnetic phase is indicated by the divergence of the static susceptibilities defined by D ab (q, iν n = 0). 31 As in Ref. [29] we study eigenvalues and eigenvectors of the 6 × 6 matrix [D ab (q, iν n )] −1 at iν n = 0.…”

Spin exchange and superconductivity in at−J′−Vmodel for two-dimensional quarter-filled systems

“…͑The full expressions for the vertices associated with the large-N approach are given in Ref. 12.͒ In Fig. 5 the Feynman rules associated with the large-N approach are summarized.…”

“…In this Appendix, we will give a summary of the pathintegral large-N approach for Hubbard operators 7,11,12 used in the present paper. A more detailed version of the formalism including the exchange coupling can be found in Ref.…”

“…͑A10͒ results from the path-integral representation of the determinant which uses the N-component boson ghost field Z p . 7,11,12 Looking at the effective Lagrangian ͑A10͒, the Feynman rules can be obtained as usual. The bilinear parts give rise to the propagators and the remaining pieces are represented by vertices.…”