We propose a self-consistent many body theory for the standard basis operator Green 's functicms and obtain an exact Lyson type matriz equation for the interacting mcmy levei systems. A zeroth order crpproximation, which neglects ali the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadvopolar system and the Hubbard model. In case of the anisotropic Heisenberg ferromagnet with both exchange and single -ion anisotropy the low-temperature renomnalization of the apin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin -1 easy plane ferromagnet, the criticai 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's like deccupling schemes. Finally, the theory is applied to the studW of the single -particle excitation spectrum of the Hubbard model.
The standard basis operators (SBO) formalism is used to study the problem of electron corre lations in narrow banda described by the Hubbard Hamiltonian, Exact Dyson equation in the matrix farm for the SBO Green's fUnction is obtained by exploiting the self consistent many body theory developed by Fedro and Wilson, and Kishore. It is feund that the present forma liam provides a natural extension of the Roth's two potes approximation scheme and reproduces the earlier spin wave results. Some inconsistencies in the Roth's scheme have also been discussed.
Self-consistent solutions of the Dyson equation are obtained using a plane-wave basis set for seven small molecules. Such self-consistent solutions can help to unify the different
GW self-consistent schemes, reduce the scatter of results in current
GW calculations, and shed light on the true effects of
GW self-consistency. Unlike other works of self-consistent
GW calculations, in the present work the Green's function is expressed as a matrix under the plane-wave basis set. The algorithmic details which enable such calculations are presented. The ability to solve the full Green's function using a plane-wave basis set may open the door for future beyond-
GW many-body perturbation theory calculations.