Large-N expansion based on the Hubbard operator path integral representation and its application to the t-J model II. The case for finite $J$

TL;DR

This paper develops a large-N perturbative approach using Hubbard operators for the t-J-V model, analyzing charge responses, phase stability, and phase transitions with respect to doping, J, and V parameters.

Contribution

It introduces a controllable large-N expansion based on Hubbard operators for the t-J-V model, enabling detailed analysis of correlation functions and phase diagrams.

Findings

Charge density responses show collective peaks more pronounced away from the particle-hole continuum.

A Fermi liquid state is stable above a critical doping δ_c, which decreases with J.

Incommensurate flux or DDW phases emerge below δ_c, and Coulomb repulsion V induces a CDW phase above V_c.

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 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-neighbors Coulomb repulsion $V$ leads to a CDW 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.