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 renormalization 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.

Starting with the $\sqrt{3}\times \sqrt{3}$ 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 $\sqrt{3}\times \sqrt{3}$ state is selected. For both the $\sqrt{3}\times \sqrt{3}$ 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...

We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength $J_1\equiv 1$, we find four magnetically ordered phases in the parameter window $J_2,J_3\in [0,1]$, namely, the Néel, striped, and Néel-II collinear AFM phases, plus a spiral phase. The Néel-II phase appears as a stable GS phase in the classical version of the model only for values $J_3<0$. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $(J_2^{c_1},J_3^{c_1})=(0.51\pm 0.01,0.69\pm 0.01)$ between the Néel, striped, and QP phases; (b) $(J_2^{c_2},J_3^{c_2})=(0.65\pm 0.02,0.55\pm 0.01)$ between the striped, spiral, and QP phases; and (c) $(J_2^{c_3},J_3^{c_3})=(0.69\pm 0.01,0.12\pm 0.01)$ between the spiral, Néel-II, and QP phases.