In this work we study the Heisenberg XXZ antiferromagnetic model for spin S and dimension d in the presence of an external longitudinal magnetic field. First, we essay a variational approach which uses as trial function a version of the analytic expression for the ground state given by the paired nonmagnetic excitation (PNME) theory [M. Lagos and G. G. Cabrera, Solid State Commun. 67, 221 (1988); Phys. Rev. B 38, 659 (1988)], generalized in order to incorporate the external field. The ground-state energy, sublattice magnetization, and magnetic susceptibility are obtained. Subsequently, we solve the problem numerically for a chain of 12 spins (S=1 and S=3/2) using the Lanczös method [E. Dagotto and A. Moreo, Phys. Rev. D 31, 865 (1985)]. The two approaches give excellent concordance over a wide range of the parameters of the model. We show that our analytic trial function represents accurately the ground state of the system for anisotropies ranging from the Ising limit to the almost isotropic Heisenberg model for all values of the field. Moreover, it accounts for the several antiferromagnetic and ferromagnetic phases occurring for different values of the magnetic field with the same precision. The critical fields of the transitions are predicted correctly. Also, results for various spin values S in two and three dimensions are presented.

• Received 14 February 1994

DOI:https://doi.org/10.1103/PhysRevB.50.242