We study the T = 0 frustrated phase of the 1D quantum spin-1 2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalisation group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.

We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spinhalf Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbour exchange bonds (J > 0 (antiferromagnetic) and −∞ < J ′ < ∞) using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Néel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Néel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants J ′ > 0. For frustrating ferromagnetic couplings J ′ < 0 we find indications that quantum fluctuations favour a first-order phase transition from the Néel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of J ′ = 0, which is equivalent to the honeycomb lattice, is treated more closely.

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a Néel model state with spins aligned in the z-direction, for both the ground-and excitedstate properties of the spin-half XXZ model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half XXZ model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUBm scheme in which we retain all k-body correlations defined on all possible locales of m adjacent lattice sites (k ≤ m).The "raw" CCM LSUBm results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUBm results to the limit m → ∞ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground-and excited-state properties of these systems across a wide range of values of the anisotropy parameter.

Starting with the √ 3 × √ 3 and the q = 0 states as reference states, we use the coupled cluster method to high orders of approximation to investigate the ground state of the Heisenberg antiferromagnet on the kagome lattice for spin quantum numbers s = 1/2, 1, 3/2, 2, 5/2, and 3. Our data for the ground-state energy for s = 1/2 are in good agreement with recent large-scale density-matrix renormalization group and exact diagonalization data. We find that the ground-state selection depends on the spin quantum number s. While for the extreme quantum case, s = 1/2, the q = 0 state is energetically favored by quantum fluctuations, for any s > 1/2 the √ 3 × √ 3 state is selected. For both the √ 3 × √ 3 and the q = 0 states the magnetic order is strongly suppressed by quantum fluctuations. Within our coupled cluster method we get vanishing values for the order parameter (sublattice magnetization) M for s = 1/2 and s = 1, but (small) nonzero values for M for s > 1. Using the data for the ground-state energy and the order parameter for s = 3/2, 2, 5/2, and 3 we also estimate the leading quantum corrections to the classical values.

We illustrate how the systematic inclusion of multi-spin correlations of the quantum spin-lattice systems can be efficiently implemented within the framework of the coupled-cluster method by examining the ground-state properties of both the square-lattice and the frustrated triangular-lattice quantum antiferromagnets. The ground-state energy and the sublattice magnetization are calculated for the square-lattice and triangular-lattice Heisenberg antiferromagnets, and our best estimates give values for the sublattice magnetization which are 62% and 51 % of the classical results for the square and triangular lattices, respectively. We furthermore make a conjecture as to why previous series expansion calculations have not indicated Neel-like long-range order for the triangular-lattice Heisenberg antiferromagnet. We investigate the critical behavior of the anisotropic systems by obtaining approximate values for the positions of phase transition points.