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.

We study the zero-temperature phase diagram of the two-dimensional quantum J 1 XXZ-J 2 XXZ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy ⌬ on the z-aligned Néel and ͑collinear͒ stripe states, as well as on the xy-planar-aligned Néel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states, on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two quantum triple points ͑QTPs͒ at ͑⌬ c = −0.10Ϯ 0.15, J 2 c / J 1 = 0.505Ϯ 0.015͒ and ͑⌬ c = 2.05Ϯ 0.15, J 2 c / J 1 = 0.530Ϯ 0.015͒, between which an intermediate magnetically disordered phase emerges to separate the quasiclassical Néel and stripe collinear phases. Above the upper QTP ͑⌬տ2.0͒ we find a direct first-order phase transition between the Néel and stripe phases, exactly as for the classical case. The z-aligned and xy-planar-aligned phases meet precisely at ⌬ = 1, also as for the classical case. For all values of the anisotropy parameter between those of the two QTPs there exists a narrow range of values of J 2 / J 1 , ␣ c 1 ͑⌬͒ Ͻ J 2 / J 1 Ͻ ␣ c 2 ͑⌬͒, centered near the point of maximum classical frustration, J 2 / J 1 = 1 2 , for which the intermediate phase exists. This range is widest precisely at the isotropic point, ⌬ = 1, where ␣ c 1 ͑1͒ = 0.44Ϯ 0.01 and ␣ c 2 ͑1͒ = 0.59Ϯ 0.01. The two QTPs are characterized by values ⌬ = ⌬ c at which ␣ c 1 ͑⌬ c ͒ = ␣ c 2 ͑⌬ c ͒.

We present evidence that crystalline Sr2Cu(PO4)2 is a nearly perfect one-dimensional (1D) spin-1/2 anti-ferromagnetic Heisenberg model (AHM) chain compound with nearest neighbor only exchange. We undertake a broad theoretical study of the magnetic properties of this compound using first principles (LDA, LDA+U calculations), exact diagonalization and Bethe-ansatz methodologies to decompose the individual magnetic contributions, quantify their effect, and fit to experimental data. We calculate that the conditions of one-dimensionality and short-ranged magnetic interactions are sufficiently fulfilled that Bethe's analytical solution should be applicable, opening up the possibility to explore effects beyond the infinite chain limit of the AHM Hamiltonian. We begin such an exploration by examining some extrinsic effects such as impurities and defects.

Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study the influence of frustration and quantum fluctuations on the magnetic ordering in the ground state of the spin-1 2 J1-J2 Heisenberg antiferromagnet (J1-J2 model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on the square lattice, we find for the bcc lattice that frustration and quantum fluctuations do not lead to a quantum disordered phase for strong frustration. The results of both approaches (ED, LSWT) suggest a first order transition at J2/J1 ≈ 0.7 from the two-sublattice Néel phase at low J2 to a collinear phase at large J2.

We investigate the phase diagram of the Heisenberg antiferromagnet on the square lattice with two different nearest-neighbor bonds J and J ′ (J-J ′ model) at zero temperature. The model exhibits a quantum phase transition at a critical value J ′ c > J between a semi-classically ordered Néel and a magnetically disordered quantum paramagnetic phase of valence-bond type, which is driven by local singlet formation on J ′ bonds. We study the influence of spin quantum number s on this phase transition by means of a variational mean-field approach, the coupled cluster method, and the Lanczos exact-diagonalization technique. We present evidence that the critical value J ′ c increases with growing s according to J ′ c ∝ s(s + 1).