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.

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling J ⊥ on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (J ⊥ = 0) we find that the phases with magnetic long-range order at small J2 < Jc 1 and large J2 > Jc 2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling J ⊥ > 0 the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small J ⊥ ∼ 0.2 − 0.3J1.The properties of the frustrated spin-1/2 Heisenberg antiferromagnet (HAFM) with nearest-neighbor J 1 and competing next-nearest-neighbor J 2 coupling (J 1 -J 2 model) on the square lattice have attracted a great deal of interest during the last fifteen years (see, e.g., Refs. 1-12 and references therein). The recent synthesis of layered magnetic materials 13,14 which can be described by the J 1 -J 2 model has stimulated a renewed interest in this model. It is well-accepted that the model exhibits two magnetically long-range ordered phases at small and at large J 2 separated by an intermediate quantum paramagnetic phase without magnetic long-range order (LRO) in the parameter region J c1 < J 2 < J c2 , where J c1 ≈ 0.4 and J c2 ≈ 0.6. The ground state (GS) at low J 2 < J c1 exhibits semi-classical Néel magnetic LRO with the magnetic wave vector Q 0 = (π, π). The GS at large J 2 > J c2 shows so-called collinear magnetic LRO with the magnetic wave vectors Q 1 = (π, 0) or Q 2 = (0, π). These two collinear states are characterized by a parallel spin orientation of nearest neighbors in vertical (horizontal) direction and an antiparallel spin orientation of nearest neighbors in horizontal (vertical) direction. The properties of the intermediate quantum paramagnetic phase are still under discussion, however, a valence-bond crystal phase seems to be most favorable. 2-4,8,9The properties of quantum magnets strongly depend on the dimensionality.15 Though the tendency to order is more pronounced in three-dimensional (3d) systems than in low-dimensional ones, a magnetically disordered phase can also be observed in frustrated 3d systems such as the HAFM on the pyrochlore lattice 16 or on the stacked kagomé lattice.17 On the other hand, recently it has been found that the 3d J 1 -J 2 model on the body-centered cubic lattice does not have an intermediate quantum paramagnetic phase.18,19 Moreover, in experimental realizations of the J 1 -J 2 model the magnetic couplings are expected to be not strictly 2d, but a finite interlayer coupling J ⊥ is present. For example, recently Rosner et al.14 have found J ⊥ /J 1 ∼ 0.07 for Li 2 VOSiO 4 , a material which can be described by a square lattice J 1 -J 2 model with large J 2 . 13,14This motivates us to consider an extension of the...

We study the phase diagram of the two-dimensional (2D) J 1-J 1-J 2 spin-1/2 Heisenberg model by means of the coupled cluster method. The effect of the coupling J 1 on the Néel and stripe states is investigated. We find that the quantum critical points for the Néel and stripe phases increase as the coupling strength J 1 is increased, and an intermediate phase emerges above the region at J 1 ≈ 0.6 when J 1 = 1. We find indications for a quantum triple point at J 1 ≈ 0.60 ± 0.03, J 2 ≈ 0.33 ± 0.02 for J 1 = 1.

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 consider the zero-temperature properties of the spin-half two-dimensional Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method (CCM) treatment. We find that this model demonstrates various ground-state phases (Néel, magnetically disordered, orthogonal dimer), and we make predictions for the positions of the phase transition points. In particular, we find that orthogonal-dimer state becomes the ground state at J

We investigate the ground-state magnetic order of the spin-1/2 J 1 -J 2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J 1 < 0 and frustrating antiferromagnetic next-nearest neighbor exchange J 2 > 0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N = 40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J c1 2 = 0.393|J 1 | (exact diagonalization) and J c1 2 = 0.394|J 1 | (coupled-cluster method). We compare our results for ferromagnetic J 1 with established results for the spin-1/2 J 1 -J 2 Heisenberg model with antiferromagnetic J 1 . We find that both models (i.e., ferro-and antiferromagnetic J 1 ) behave similarly for large J 2 , although significant differences between them are observed for J 2 /|J 1 | 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J c2 2 ≈ 0.6J 1 for antiferromagnetic J 1 , we do not find a similar breakdown of this kind of long-range order until J 2 ∼ 0.4|J 1 | for the model with ferromagnetic J 1 . Unlike the case for antiferromagnetic J 1 , if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J 1 then it is likely to be over a very small range below J 2 ∼ 0.4|J 1 |.PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 75.10.Kt Quantum spin liquids, valence bond phases and related phenomena

We present results for a complementary analysis of the frustrated planar J 1 -J 2 -J 3 spin-1/2 quantum antiferromagnet (AFM). Using dynamical functional renormalization group, high-order-coupled cluster calculations, and series expansion based on the flow equation method, we have calculated generalized momentum-resolved susceptibilities, the ground-state energy, the magnetic-order parameter, and the elementary excitation gap. From these, we determine a quantum phase diagram that shows a large window of a quantum paramagnetic (QP) phase situated among the Néel, spiral, and collinear states, which are present already in the classical J 1 -J 2 -J 3 AFM. Our findings are consistent with substantial plaquette correlations in the QP phase. The extent of the QP region is found to be in satisfying agreement between the three different approaches we have employed.

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.