Generalized dynamical random phase approximation for the collective Green's function of the anisotropic Heisenberg ferromagnet

A generalized (symmetrized) random phase approximation for the collective Green's function is considered; it is based on the Fourier transforms of the operators of the spin density and uses the Hartree–Fock renormalization of the single-particle spectrum. This is then used in the long-wavelength approximation to find the longitudinal static component of the susceptibility tensor and the longitudinal correlation function of an anisotropic Heisenberg ferromagnet of the easy axis type, and low-temperature expansions of the corresponding quantities are constructed. It is shown that the employed approximations are consistent; in particular, because of the presence of the kinematic interaction they lead (in the lowest approximation in the magnon density) to compensation of the “collective” contributions, so that the renormalization of the susceptibility and the correlation function is determined solely by the “single-particle”' dynamical contributions.