Cluster-variation approach to the spin-1/2<i>XXZ</i>model

Abstract

We use the cluster-variation method to examine the phase diagram of the spin-1/2 XXZ model. The clusters used consist of two neighboring spins. With this method, we calculate global phase diagrams for arbitrary values of the anisotropy ${\mathit{J}}_{\mathit{z}}$/J and for arbitrary external magnetic fields. Lattices with different values of the coordination number z are considered. Analytic expressions are found for nearly all phase boundaries; the remaining phase boundary is located numerically. Despite some problems at low temperature, the results based on this approach are in quite good agreement with the results from series-expansion methods. A connection is made with the Hubbard model, which can be mapped onto the XXZ Hamiltonian in the limit of strong on-site attraction.