Problem: Anisotropic Heisenberg Model

    The anisotropic Heisenberg model is defined by the Hamiltonian

Consider a one-dimensional system with nearest-neighbor interactions.

and ferromagnetic coupling, J;SPMgt;0, J';SPMgt;0.

(a) Show that for J';SPMgt;J the magnon wavefunctions are similar to the isotropic Heisenberg model solutions, but they have a nonzero energy at k=0.

(b) Show that for J';SPMlt;J the ferromagnetically ordered state (with magnetization aligned in the z direction) is not the ground state of the Hamiltonian.