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

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

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

Rapid immigrant suburbanization means that for many, segregation has shifted to the periphery.

As of 2010, over half of the U.S. foreign population was located in the suburbs, with just one third living in cities. But how has suburban segregation affected these immigrants? In new research which examines immigrant suburbanization patterns, Chad R. Farrell finds that many immigrants experience a great degree of segregation in the suburbs. Immigrants from Canada, Germany, and the UK experience the lowest levels of segregation, while Latin American and Caribbean immigrants experience the highest

Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets

The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular lattices is studied using the coupled cluster method (CCM) technique of quantum many-body theory. The phase relations between different expansion coefficients of the ground-state wave function in an Ising basis for the square lattice HAF is exactly known via the Marshall-Peierls sign rule, although no equivalent sign rule has yet been obtained for the triangular lattice HAF. Here the CCM is used to give accurate estimates for the Ising-expansion coefficients for these systems, and CCM results are noted to be fully consistent with the Marshall-Peierls sign rule for the square lattice case. For the triangular lattice HAF, a heuristic rule is presented which fits our CCM results for the Ising-expansion coefficients of states which correspond to two-body excitations with respect to the reference state. It is also seen that Ising-expansion coefficients which describe localised, $m$-body excitations with respect to the reference state are found to be highly converged, and from this result we infer that the nodal surface of the triangular lattice HAF is being accurately modeled. Using these results, we are able to make suggestions regarding possible extensions of existing quantum Monte Carlo simulations for the triangular lattice HAF.Comment: 24 pages, Latex, 3 postscript figure

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

Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet

The coupled cluster method is applied to a spin-half model at zero temperature ($T=0$), which interpolates between Heisenberg antiferromagnets (HAF's) on a kagome and a square lattice. With respect to an underlying triangular lattice the strengths of the Heisenberg bonds joining the nearest-neighbor (NN) kagome sites are $J_{1} \geq 0$ along two of the equivalent directions and $J_{2} \geq 0$ along the third. Sites connected by $J_{2}$ bonds are themselves connected to the missing NN non-kagome sites of the triangular lattice by bonds of strength $J_{1}' \geq 0$. When $J_{1}'=J_{1}$ and $J_{2}=0$ the model reduces to the square-lattice HAF. The magnetic ordering of the system is investigated and its $T=0$ phase diagram discussed. Results for the kagome HAF limit are among the best available.Comment: 21 pages, 8 figure