J. Schulenburg

Diamond chains with multiple-spin exchange interactions

We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic fourfold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed as well.

Frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice studied via exact diagonalization and coupled-cluster method

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. 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 = 0.393jJ1j(exact diagonalization) and J c1 2 = 0.394jJ1j(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/jJ1j. 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J c2 2 � 0.6J1 for antiferromagnetic J1, we do not find a similar breakdown of this kind of long-range order until J2 � 0.4jJ1jfor 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 � 0.4jJ1j.

Tight-binding parameters and exchange integrals of Ba 2 Cu 3 O 4 Cl 2

Band-structure calculations of Ba2Cu3O4Cl2 within the local-density approximation ~LDA! are presented. The investigated compound is similar to the antiferromagnetic parent compounds of the cuprate superconductors but contains additional CuB atoms in the Cu-O planes. Within the LDA, metallic behavior is found with two bands crossing the Fermi surface. These bands are built mainly from Cu 3dx22y 2 and O2 p x , y orbitals, and a corresponding tight-binding ~TB! model for these bands has been parameterized. All orbitals can be subdivided in two sets corresponding to the A and B subsystems, respectively, the coupling between which is found to be small. To describe the experimentally observed antiferromagnetic insulating state, we propose an extended Hubbard model using the parameters derived from the TB fit and local correlation terms characteristic for cuprates. Using this parameter set we calculate the exchange integrals for the Cu 3O4 plane, the results being in quite reasonable agreement with the experimental values for the isostructural compound Sr 2Cu3O4Cl2. @S0163-1829~98!009222-9#

Ground-state phase diagram of the spin-12square-latticeJ1-J2model with plaquette structure

Using the coupled cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-1/2 J1-J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (J1>0) as well as ferromagnetic (J1 0. The strength of inter-plaquette interaction lambda varies between lambda=1 (that corresponds to the uniform J1-J2 model) and lambda=0 (that corresponds to isolated frustrated 4-spin plaquettes). While on the classical level (s \to \infty) both versions of models (i.e., with ferro- and antiferromagnetic J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case s=1/2. For the antiferromagnetic case (J1 > 0) Neel antiferromagnetic long-range order at small J2/J1 and lambda \gtrsim 0.47 as well as collinear striped antiferromagnetic long-range order at large J2/J1 and lambda \gtrsim 0.30 appear which correspond to their classical counterparts. Both semi-classical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing of lambda. For the ferromagnetic case (J1 < 0) we have the trivial ferromagnetic ground state at small J2/|J1|. By increasing of J2 this classical phase gives way for a semi-classical plaquette phase, where the plaquette block spins of length s=2 are antiferromagnetically long-range ordered. Further increasing of J2 then yields collinear striped antiferromagnetic long-range order for lambda \gtrsim 0.38, but a nonmagnetic quantum paramagnetic phase lambda \lesssim 0.38.

Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: high-order coupled-cluster calculations

Abstract.We investigate the ground-state magnetic long-range order of quasi-one-dimensional quantum Heisenberg antiferromagnets for spin quantum numbers s = 1/2 and s = 1. We use the coupled cluster method to calculate the sublattice magnetization and its dependence on the inter-chain coupling J⊥. We find that for the unfrustrated spin-1/2 system, an infinitesimal inter-chain coupling is sufficient to stabilize magnetic long-range order, in agreement with results obtained by other methods. For s = 1, we find that a finite inter-chain coupling is necessary to stabilize magnetic long-range order. Furthermore, we consider a quasi one-dimensional spin-1/2 system, where a frustrating next-nearest neighbor in-chain coupling is included. We find that for stronger frustration as well, a finite inter-chain coupling is necessary to have magnetic long-range order in the ground state, and that the strength of the inter-chain coupling necessary to establish magnetic long-range order is related to the size of the spin gap of the isolated chain.

Ground state and low-lying excitations of the spin-1/2 XXZ model on the Kagomé lattice at magnetization 1/3

Abstract We study the ground state and low-lying excitations of the S = 1 2 XXZ antiferromagnet on the kagome lattice at magnetization one-third of the saturation. An exponential number of non-magnetic states is found below a magnetic gap. The non-magnetic excitations also have a gap above the ground state, but it is much smaller than the magnetic gap. This ground state corresponds to an ordered pattern with resonances in one-third of the hexagons. The spin–spin correlation function is short ranged, but there is long-range order of valence-bond crystal type.

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half {\it XXZ} antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ 1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart.

Magnetic model for Ba 2Cu3O4Cl2

Abstract Ba 2 Cu 3 O 4 Cl 2 consists of two types of copper atoms, Cu(A) and Cu(B). We study the corresponding Heisenberg model with three antiferromagnetic couplings, J AA , J BB and J AB . We find interesting frustration effects due to the coupling J AB .

Phase transitions in two-layer spin 12 antiferromagnets with competing intra-layer and inter-layer couplings

Abstract We study the phase diagram of layered spin 1 2 antiferromagnets with long-range and short-range inter-layer coupling. We discuss quantum disorder in the short-range model and order from disorder phenomena in the long range model.