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 investigate ground states of s=1/2 Heisenberg antiferromagnets on the eleven twodimensional (2D) Archimedian lattices by using the coupled cluster method. Magnetic interactions and quantum fluctuations play against each other subtly in 2D quantum magnets and the magnetic ordering is thus sensitive to the features of lattice topology. Archimedean lattices are those lattices that have 2D arrangements of regular polygons and they often build the underlying magnetic lattices of insulating quasi-two-dimensional quantum magnetic materials. Hence they allow a systematic study of the relationship between lattice topology and magnetic ordering. We find that the Archimedian lattices fall into three groups: those with semiclassical magnetic groundstate long-range order, those with a magnetically disordered (cooperative quantum paramagnetic) ground state, and those with a fragile magnetic order. The most relevant parameters affecting the magnetic ordering are the coordination number and the degree of frustration present.

We use the coupled cluster method to high orders of approximation in order to calculate the ground-state phase diagram of the XXZ spin-s kagome antiferromagnet with easy-plane anisotropy, i.e. the anisotropy parameter ∆ varies between ∆ = 1 (isotropic Heisenberg model) and ∆ = 0 (XY model). We find that for the extreme quantum case s = 1/2 the ground state is magnetically disordered in the entire region 0 ≤ ∆ ≤ 1. For s = 1 the ground state is disordered for 0.818 < ∆ ≤ 1, it exhibits √ 3 × √ 3 magnetic long-range order for 0.281 < ∆ < 0.818, and q = 0 magnetic longrange order for 0 ≤ ∆ < 0.281. We confirm the recent result of Chernyshev and Zhitomirsky (Phys. Rev. Lett. 113, 237202 (2014)) that the selection of the ground state by quantum fluctuations is different for small ∆ (XY limit) and for ∆ close to one (Heisenberg limit), i.e., q = 0 magnetic order is favored over √ 3 × √ 3 for 0 ≤ ∆ < ∆c and vice versa for ∆c < ∆ ≤ 1. We calculate ∆c as a function of the spin quantum number s.

We use the coupled cluster method implemented to high orders of approximation to investigate the frustrated spin-1 2 J 1-J 2-J 3 antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength J 1 > 0 between nearest-neighbor pairs, J 2 > 0 between next-nearest neighbor pairs, and J 3 > 0 between nextnext-nearest-neighbor pairs of spins. In particular, we study both the ground-state (GS) and lowest-lying triplet excited-state properties in the case J 3 = J 2 ≡ κJ 1 , in the window 0 κ 1 of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at κ cl = 1 2. We present GS results for the spin stiffness ρ s and the zero-field uniform magnetic susceptibility χ , which complement our earlier results for the GS energy per spin E/N and staggered magnetization M to yield a complete set of accurate low-energy parameters for the model. Our results all point towards a phase diagram containing two quasiclassical antiferromagnetic phases, one with Néel order for κ < κ c 1 , and the other with collinear striped order for κ > κ c 2. The results for both χ and the spin gap provide compelling evidence for a disordered quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region κ c 1 < κ < κ c 2 , especially close to the two quantum critical points at κ c 1 and κ c 2. Each of our fully independent sets of results for the low-energy parameters is consistent with the values κ c 1 = 0.45 ± 0.02 and κ c 2 = 0.60 ± 0.02, and with the transition at κ c 1 being of continuous (and hence probably of the deconfined) type and that at κ c 2 being of first-order type.

We apply the coupled cluster method to high orders of approximation and exact diagonalizations to study the ground-state properties of the triangular-lattice spin-s Heisenberg antiferromagnet.We calculate the fundamental ground-state quantities, namely, the energy e 0 , the sublattice magnetization M sub , the in-plane spin stiffness ρ s and the in-plane magnetic susceptibility χ for spin quantum numbers s = 1/2, 1, . . . , s max , where s max = 9/2 for e 0 and M sub , s max = 4 for ρ s and s max = 3 for χ. We use the data for s ≥ 3/2 to estimate the leading quantum corrections to the classical values of e 0 , M sub , ρ s , and χ. In addition, we study the magnetization process, the width of the 1/3 plateau as well as the sublattice magnetizations in the plateau state as a function of the spin quantum number s.