Quantum J1J_1--J2J_2 antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.Comment: 4 pages, 3 figure

Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagom\'e lattice

We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagom\'e lattices by using the spin-rotation-invariant Green's function method. We calculate the critical temperature $T_C$, the uniform static susceptibility $\chi$, the correlation lengths $\xi_\nu$ and the magnetization $M$ and investigate the short-range order above $T_C$. We find that $T_C$ and $M$ at $T>0$ are smaller for the stacked kagom\'e lattice which we attribute to frustration effects becoming relevant at finite temperatures.Comment: shortened version as published in PR

The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study

We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>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 J2^{c1}=0.393|J1| (exact diagonalization) and J2^{c1}=0.394|J1| (coupled-cluster method). We compare our results for ferromagnetic J1 with established results for the spin-1/2 J1-J2 Heisenberg model with antiferromagnetic J1. We find that both models (i.e., ferro- and antiferromagnetic J1) behave similarly for large J2, although significant differences between them are observed for J2/|J1| \lesssim 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J2^{c2} \approx 0.6J1 for antiferromagnetic J1, we do not find a similar breakdown of this kind of long-range order until J2 \sim 0.4|J1| for the model with ferromagnetic J1. Unlike the case for antiferromagnetic J1, if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J1 then it is likely to be over a very small range below J2 \sim 0.4|J1|.Comment: 15 pages, 7 figures, 2 table

High-Order Coupled Cluster Calculations Via Parallel Processing: An Illustration For CaV4_4O9_9

The coupled cluster method (CCM) is a method of quantum many-body theory that may provide accurate results for the ground-state properties of lattice quantum spin systems even in the presence of strong frustration and for lattices of arbitrary spatial dimensionality. Here we present a significant extension of the method by introducing a new approach that allows an efficient parallelization of computer codes that carry out ``high-order'' CCM calculations. We find that we are able to extend such CCM calculations by an order of magnitude higher than ever before utilized in a high-order CCM calculation for an antiferromagnet. Furthermore, we use only a relatively modest number of processors, namely, eight. Such very high-order CCM calculations are possible {\it only} by using such a parallelized approach. An illustration of the new approach is presented for the ground-state properties of a highly frustrated two-dimensional magnetic material, CaV$_4$O$_9$. Our best results for the ground-state energy and sublattice magnetization for the pure nearest-neighbor model are given by $E_g/N=-0.5534$ and $M=0.19$, respectively, and we predict that there is no N\'eel ordering in the region $0.2 \le J_2/J_1 \le 0.7$. These results are shown to be in excellent agreement with the best results of other approximate methods.Comment: 4 page

Influence of the spin quantum number ss on the zero-temperature phase transition in the square lattice JJ-J′J' model

We investigate the phase diagram of the Heisenberg antiferromagnet on the square lattice with two different nearest-neighbor bonds $J$ and $J'$ ($J$-$J'$ model) at zero temperature. The model exhibits a quantum phase transition at a critical value $J'_c > J$ between a semi-classically ordered N\'eel and a magnetically disordered quantum paramagnetic phase of valence-bond type, which is driven by local singlet formation on $J'$ bonds. We study the influence of spin quantum number $s$ on this phase transition by means of a variational mean-field approach, the coupled cluster method, and the Lanczos exact-diagonalization technique. We present evidence that the critical value $J'_c$ increases with growing $s$ according to $J'_c \propto s(s+1)$.Comment: 13 pages, 6 figure

The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue

We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J_1-J_2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J_2^{c1}=0.454J_1 and J_2^{c2}= 0.588 J_1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J_2 \le 0.49J_1 and J_2 > 0.58J_1. This finding is in favor of a gapless spin-liquid ground state in this parameter regime.Comment: 10 pages, 3 figures, accepted versio