THE HUBBARD OPERATORS AND THE SLAVE-PARTICLES PATH-INTEGRAL REPRESENTATIONS DESCRIBING THE t-J MODEL

In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson decoupled representation.

WEAK-COUPLING PHASE DIAGRAM OF THE ONE-DIMENSIONAL DEFORMED T-J MODEL

The deformed t-J lattice model is defined by replacing the fermion operators by the deformed Hubbard operators in the t-term but without changing the J-term in the conventional t-J model. The physics of this model was argued to be continuously connected to those of the t-J one when the deformation parameter λ varies from zero to unit. In this paper, by using the bosonization field theory and renormalization group technique, we study the phase diagram of the one dimension deformed t-J model in the regime where λ and J/t are both positively small but comparable to each other. By explicitly incorporating the contributions from the deformation-induced six-particle term and the antiferromagnetic exchange interaction, we find that at half-filling the system shows three distinct ground states characterized by the Luttinger liquid, the spin-density-wave and the bond-order-wave, respectively. These results indicate that the ground state phases of the deformed t-J model is neither connected smoothly to those of the system at λ = 1 nor to those of the conventional t-J model.

DIAGRAMMATICS AND FEYNMAN RULES IN THE LAGRANGIAN THEORY BASED ON THE spl(2,1) GRADED ALGEBRA

From the path-integral method, the diagrammatics and Feynman rules for the Lagrangian theory based on the spl(2,1) graded algebra are constructed. The first-order Lagrangian we have obtained is written in terms of the graded Hubbard operators. By using functional techniques, the correlation generating functional is given in terms of the proper effective Lagrangian of the model. Once the Feynman rules, propagators and vertices were found, a physical discussion about the free propagators is given. Finally, the expressions of the boson self-energy and the renormalized boson propagator are used to study the hole effects on the magnetic properties of the high-T c cuprates.

ELECTRONIC STRUCTURE FOR THE TWO-BAND HUBBARD MODEL OF THE LADDER α′-NaV2O5 COMPOUND

An effective Hubbard model for one-particle d-like states and two-particle singlet states is derived in order to describe the low-energy electronic spectrum in ladder α′- NaV 2 O 5 compound. The energy shifts and the renormalized hopping parameters for the considered electronic states are calculated on the basis of the projection technique for the two-time matrix Green's function in terms of Hubbard operators.