Green Function Technique in the Theory of Strongly Correlated Systems

Abstract

In the past few years there has been a growing interest in the Hubbard model [I] and its limiting case -the (t-J) model [2,3] owing to the idea of a possible non-phonon mechanism of high-l", superconductivity in copper oxide compounds, which are strongly correlated systems [4]. However, investigations in this field are conducted mainly for two-dimensional models near the half-filling case. At the same time, the general problem of possible magnetic states in these models is very far from being resolved. Recently Izyumov et al. [5, 61 have studied the Hubbard model in the limit of strong Coulomb interaction (the (t-J) model) by the diagram technique for Hubbard operators. The dynamic magnetic and dielectric susceptibilities are calculated.The aim of this note is to study the magnetic properties of the (t-J) model using a Green function technique in a wide interval of electron concentrations, 0 < n < 1, and also to go beyond the random phase approximation. The standard Hubbard model is given by the following Hamiltonian:It is known that in the case of strong Coulomb repulsion (U %-t) one can pass from the general Hamiltonian (1) (4) ,,,(x; +x; --x: +x, -) . If'Here E, = -(oh/2) -,u is the energy of a one-electron state on a site, p the chemical potential, h = gpBH, H the magnetic field, and J = t'/U the effective exchange integral.') Blvd. J. Bouchier 5, BG-1126 Sofia, Bulgaria.