Antiferromagnetic long-range order in the anisotropic quantum spin chain

This is a study of the ground-state properties of the one-dimensional spin-s(12⩽s<∞) anisotropic XYZ antiferromagnet in a magnetic field of arbitrary direction. It provides the first rigorous results for the general case of this model in non-zero field. By exact calculations we find the existence of an ellipsoidal surface h = hN in field space where the ground state is of the classical two-sublattice Néel type with non-zero antiferromagnetic long-range order. At hN there are no correlated quantum fluctuations. We give upper and lower bounds for the critical field hc where antiferromagnetic long-range order is suppressed by the field. The zero-temperature phase diagrams are discussed for a few representative cases.