Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J 1 -J 2 frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the Néel and collinear orders are J 2 c1 Ϸ͑0.44Ϯ 0.01͒J 1 and J 2 c2 Ϸ͑0.59Ϯ 0.01͒J 1 , respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by ͓Sirker et al. Phys. Rev. B 73, 184420 ͑2006͔͒, our data do not provide evidence for the transition from the Néel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Approximate methods are difficult to apply to the triangular-lattice antiferromagnet because of frustration, and so, for example, the quantum Monte Carlo (QMC) method suffers from the "sign problem." Results for this model in the presence of magnetic field are rarer than those for the square-lattice system. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the 'LSUBm' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of χ = 0.070 for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., χ = 0.0669 via QMC). Our estimate for the range of the extent of the (M/M s =) 1 3 magnetisation plateau for the triangular-lattice antiferromagnet is 1.37 < λ < 2.15, which is in good agreement with results of spin-wave theory (1.248 < λ < 2.145) and exact diagonalisations (1.38 < λ < 2.16). Our results therefore support those of exact diagonalisations that indicate that the plateau begins at a higher value of λ than that suggested by spin-wave theory. The CCM value for the in-plane magnetic susceptibility per site is χ = 0.065, which is below the result of the spin-wave theory (evaluated to order 1/S) of χ SW T = 0.0794. Higher order calculations are thus suggested for both SWT and CCM LSUBm calculations in order to determine the value of χ for the triangular lattice conclusively.2

Using the coupled cluster method for high orders of approximation and Lanczos exact diagonal-ization we study the ground-state phase diagram of a quantum spin-1/2 J1-J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (J1 > 0) as well as ferromagnetic (J1 < 0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction J2 > 0. The strength of inter-plaquette interaction λ varies between λ = 1 (that corresponds to the uniform J1-J2 model) and λ = 0 (that corresponds to isolated frustrated 4-spin plaquettes). While on the classical level (s → ∞) both versions of models (i.e., with ferro-and antiferromagnetic J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case s = 1/2. For the antiferromagnetic case (J1 > 0) Néel antiferromagnetic long-range order at small J2/J1 and λ 0.47 as well as collinear striped an-tiferromagnetic long-range order at large J2/J1 and λ 0.30 appear which correspond to their classical counterparts. Both semi-classical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing of λ. For the ferromagnetic case (J1 < 0) we have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of J2 this classical phase gives way for a semi-classical pla-quette phase, where the plaquette block spins of length s = 2 are antiferromagnetically long-range ordered. Further increasing of J2 then yields collinear striped antiferromagnetic long-range order for λ 0.38, but a nonmagnetic quantum paramagnetic phase λ 0.38.

We investigate the antiferromagnetic canting instability of the spin-1/2 kagome ferromagnet, as realized in the layered cuprates Cu3Bi(SeO3)2O2X (X=Br, Cl, and I). While the local canting can be explained in terms of competing exchange interactions, the direction of the ferrimagnetic order parameter fluctuates strongly even at short distances on account of frustration which gives rise to an infinite ground state degeneracy at the classical level. In analogy with the kagome antiferromagnet, the accidental degeneracy is fully lifted only by non-linear 1/S corrections, rendering the selected uniform canted phase very fragile even for spins-1/2, as shown explicitly by coupled-cluster calculations. To account for the observed ordering, we show that the minimal description of these systems must include the microscopic Dzyaloshinsky-Moriya interactions, which we obtain from densityfunctional band-structure calculations. The model explains all qualitative properties of the kagome francisites, including the detailed nature of the ground state and the anisotropic response under a magnetic field. The predicted magnon excitation spectrum and quantitative features of the magnetization process call for further experimental investigations of these compounds.

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