The coupled-cluster method (CCM) is applied to anisotropic-quantum-antiferromagnetic models in one and two dimensions (1D and 2D). Several hierarchical approximation schemes of the CCM are de6ned, which are specialized for the spin-lattice models. Good results are obtained for both groundstate and excited-state energies. The spin-spin correlation functions and the staggered magnetizations are also calculated. We have found that the CCM gives a qualitatively correct description of the entire Heisenberg-Ising phase, including the critical point where a phase transition occurs in 1D. Some interesting differences between 1D and 2D models near the critical point are discussed.

We apply the microscopic coupled-cluster method (CCM) to the spin-1 2 XXZ models on both the one-dimensional chain and the two-dimensional square lattice. Based on a systematic approximation scheme of the CCM developed by us previously, we carry out high-order ab initio calculations using computer-algebraic techniques. The ground-state properties of the models are obtained with high accuracy as functions of the anisotropy parameter. Furthermore, our CCM analysis enables us to study their quantum critical behavior in a systematic and unbiased manner.

Some rigorous results are presented for a first-order quantum phase transition between the dimerized state and Haldane-type state (i.e., a state similar to the ground state of the one-dimensional spin-1 Heisenberg chain) in the spin-1/2 coupled chains with nearest-neighbour and next-nearestneighbour Heisenberg interactions. Also presented are the exact excited states in both phases. A partial phase diagram of the general spin-1/2 coupled chains is discussed.

The spontaneous dimerization of the frustrated spin-1 2 antiferromagnetic chains is studied by a microscopic approach based on a proper set of composite operators (i.e., pseudo-spin operators). Two approximation schemes are developed. Firstly, a spin-wave approximation is made by a Dyson-Maléev-like boson transformation. The ground-state properties and the triplet excitation spectra are obtained as functions of the coupling parameter. Secondly, based on the pseudo-spin operators, a microscopic treatment is formulated within the framework of the powerful, systematic coupled-cluster method (CCM). Comparison between various approximations is made. The advantage of the CCM for the purposes of systematic improvement is emphasized.

The coupled-cluster method of many-body theory is applied to anisotropic quantum antiferromagnets in one and two dimensions.It is found to give good results for ground-state and excited-state energies and the staggered magnetization.