The t-J model is analyzed in the context of the path-integral formalism. The starting point is the first-order Lagrangian formulation written in terms of the Hubbard operators recently developed. Subsequently, by using functional techniques the correlation generating functional is constructed in terms of the proper effective Lagrangian of the model. Next, for small hole density and considering an antiferromagnetic background, a perturbative treatment of the effective Lagrangian is carried out, and so the diagrammatics and the Feynman rules can be found. Finally, the Feynman rules, propagators, and vertices are used to study magnetic properties.
2000 Academic Press
I. INTRODUCTION
In two recent papers [1, 2] the classical and quantum Lagrangian dynamics for the SU(2) bosonic algebra and for the general graded algebra spl(2,1) were analyzed. In both cases a family of first-order Lagrangians written in terms of the Hubbard X -operators was found. So, the field variables are directly the Hubbard X -operators satisfiying the algebra under consideration. In our approach the Hubbard X -operators representing the real physical excitations are treated as indivisible objects and any decoupling is used.
In the pure bosonic case (see Ref.
[1]), from a classical first-order Lagrangian describing the Heisenberg model, and by means of the path-integral techniques, the perturbative quantum formalism was developed.
As it is known, the most important model at present to treat strongly correlated electrons is the t-J model, and it is a good candidate to explain the high-Tc superconductivity [3]. The mathematical basis of this model is contained in the graded algebra spl(2,1). In Ref. [2] a new discussion about the construction of a family of first-order Lagrangians describing the dynamics of the t-J model was presented. This constrained system was treated in the framework of the symplectic Faddeev Jackiw formalism. As it was shown, the set of possible constraints is naturally provided by the symplectic formalim.
Once the constraint structure is found the t-J model can be studied by using functional techniques. In this context the correlation generating functional is constructed