A coupled-cluster study of the ground-state energy and properties of an anisotropic quantum spin lattice model exhibiting antiferromagnetism in various phases

Abstract

We extend the domain of applicability of the coupled-cluster method (CCM) to include quantum-mechanical spin-1/2 systems on discrete lattices. We study the specific case of anisotropic antiferromagnetic interactions described by the nearest-neighbour XXZ-model Hamiltonian. The isotropic version of this model on a two-dimensional (2-d) square lattice is of great current interest as a possible description of the interactions between the electrons in the singly-occupied $$d_{x^2 - y^2 } $$ orbitals on the copper atoms in the ceramic copper oxide materials displaying high-temperature superconductivity. Although very few exact results are known for the 2-d XXZ-model, its 1-d counterpart has been exactly solved by Bethe-ansatz techniques, and we therefore use it here as a benchmark for our new CCM techniques. Even starting with the classical Neel state as the model reference state, we find that the CCM is capable at relatively low levels of truncation of giving accurate values for the ground-state energies. In this regard, we discuss several new CCM truncation hierarchies which have not previously been applied to either atoms and molecules or continuous extended systems. Furthermore, the method gives a good qualitative description of most of the known or anticipated behaviour of the correlation functions, order parameters, and elementary excitations over an entire (zero-temperature) phase, right up to the transition point, as the anisotropy is varied.