Excitations and long-range order in quadrupolar-coupled system at zero temperature

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Abstract
A spin-1 system with isotropic quadrupolar coupling is analyzed by the method of double-time Green's functions. A consistent decoupling procedure, which exactly preserves two important spin-correlation sum rules, is constructed. The resulting self-consistent integral expressions are solved numerically for the case of a simple-cubic lattice with nearest-neighbor coupling and the ground-state energy, the long-range-order parameter, and the dispersion relation of the elementary excitations are evaluated. Our result for the ground-state energy is found to be somewhat lower than that obtained by using the decoupling procedures of Raich-Etters and Barma. On the other hand, our result for the zero-point defect for the quadrupolar long-range order is very slightly greater than that given by the Raich and Etters's random-phase-approximation (RPA) procedure but is distinctly smaller than that found by properly evaluating the expressions obtained by using the Barma procedure. Similarly, our results for the elementary excitation dispersion are also closer to the RPA predictions than those obtained via the Barma procedure.