tJ-MODEL IN TERMS OF EQUATIONS WITH VARIATIONAL DERIVATIVES

Abstract

For a tJ -model in the X -operators representation a generating functional of the field describing fluctuations of matrix elements of electron hopping on a lattice is presented. The first order functional derivative with respect to this field determines the electron Green function, while the second order derivatives determine the boson Green functions of collective excitations in the system. Thus, the Kadanoff-Baym approach in the theory of fermi system with a weak Coulomb interaction is generalized on the opposite limit of systems with strong correlations. A chain of equations for different order variational derivatives were obtained, and a method was suggested based on iterations over the parameters of a tJ -model: the hopping matrix element and the exchange integral. This approach corresponds to a self-consistent Born approximation, not for the effective but for the original Hamiltonian. A scheme of calculation of the dynamical spin susceptibility is analyzed with self-consistent corrections of the first and second order. Connection of this approach with the diagram technique for X -operators is discussed.