1–J2 spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D

We study the phase diagram of the isotropic J1–J ′ 1–J2 Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled-cluster method. We find no evidence for an intermediate phase between the Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at J ′ 1/J1 ≈ 0.66± 0.03, J2/J1 ≈ 0.35± 0.02, where a line of second-order phase transitions between the quasi-classical Néel and stripe-ordered phases (for J ′ 1/J1 0.66) meets a line of first-order phase transitions between the same two states (for J ′ 1/J1 0.66). Copyright c © EPLA, 2008 Over the last 20 years or so much theoretical effort [1–8] has been expended on the J1–J2 model in which the spins situated on the sites of a two-dimensional (2D) square lattice interact via competing isotropic Heisenberg interactions between the nearest-neighbour (J1) and nextnearest-neighbour (J2) pairs. The exchange bonds J1 > 0 promote antiferromagnetic order, while the J2 > 0 bonds act to frustrate or compete with this order. Such frustrated quantum magnets continue to be of interest because of the possible spin-liquid and other such novel phases that they can exhibit (see, e.g., ref. [9]). The syntheses of compounds that can be closely described by the spin-1/2 version of the model, such as Li2VO(Si,Ge)O4 [10] and VOMoO4 [11] have further fuelled theoretical interest. It is now widely accepted that the spin-1/2 J1–J2 model on the 2D square lattice has a ground-state phase diagram showing two phases with quasi-classical long-range order (LRO) (viz., a Néelordered phase at small values of J2/J1 and a collinear stripe-ordered phase at large values of J2/J1), separated by an intermediate quantum paramagnetic phase without magnetic LRO in the parameter regime α c <α<α 2 c , where α≡ J2/J1 and α 1 c ≈ 0.4, α 2 c ≈ 0.6. Furthermore, it has been argued recently that the quantum phase transition between the quasi-classical Néel phase and the quantum paramagmetic phase present in the 2D J1–J2 model is not described by a Ginzburg-Landau–type critical theory, but rather may exhibit a deconfined quantum critical point [12]. Other authors [13] have argued that the transition is not of this second-order type due to the deconfinement of the fractionally charged spinons, but is rather a (weakly) first-order transition between the Néel phase and a valence-bond solid phase with columnar dimerisation. Such frustrated quantum magnets often have ground states that are macroscopically degenerate. This feature leads naturally to an increased sensitivity of the underlying Hamiltonian to the presence of small perturbations. In particular, the presence of anisotropies in real systems that are well characterised by the J1–J2 model, either in spin space or in real space, naturally raises the issue of how robust are the properties of the J1–J2 model against any such perturbations. There have been several recent studies addressing this question. For example, in the case of spin anisotropies, generalisations of the J1–J2 model have been studied for the spin-1/2 case, in which either the frustrating next-nearest-neighbour interaction or the nearest-neighbour interaction is anisotropic [14,15]. In the alternative case of real-space anisotropies, for example, a recent study [16] investigated the effects of including an interlayer coupling (J⊥) for the spin-half J1–J2 model on a stacked square lattice. In a previous paper of our own [17] we moved instead in the direction of one-dimensionality by investigating a spin-half spatially