Self-consistent many-body theory for the standard basis operator Green's functions

We propose a self-consistent many-body theory for the standard basis operator Green's functions and obtain an exact Dyson-type matrix equation for the interacting many-level systems. A zeroth order approximation, which neglects all the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadrupolar system and the Hubbard model. In the case of the anisotropic Heisenberg ferromagnet with both exchange and single-ion anisotropy the low-temperature renormalization of the spin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin-1 easy-plane ferromagnet, the critical parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin-1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen-like decoupling schemes. Finally, the theory is applied to the study of the single-particle excitation spectrum of the Hubbard model.