Magnetic order in the Shastry-Sutherland model

The ground state properties of the Shastry-Sutherland model in the presence of an external field are investigated by means of variational states built up from unpaired spins (monomers) and singlet pairs of spins (dimers). The minimum of the energy is characterized by specific monomer-dimer configurations, which visualize the magnetic order in the sectors with fixed magnetization M=S/N. A change in the magnetic order is observed if the frustrating coupling alpha exceeds a critical value alpha_c(M), which depends on M. Special attention is paid to the ground state configurations at M=1/4, 1/6, 1/8.Comment: 9 pages, 9 figures, RevTe

The magnetization process in the 2-dimensional J_1-J_2 model

We study the alpha = J_2/J_1-dependence of the magnetization process in the J_1-J_2 model on a square lattice with frustrating couplings J_2 along the diagonals. Perturbation expansions around alpha=J_2/J_1=0 and 1/alpha=0$ yield an adequate description of the magnetization curve in the antiferromagnetic and collinear antiferromagnetic phase, respectively. The transition from one phase to the other (0.5 < alpha < 0.7) leaves pronounced structures in the longitudinal and transverse structure factors at p=(pi,pi) and p=(0,pi).Comment: 10 pages, 10 figures, RevTe

Charge density plateaux and insulating phases in the t−Jt-J model with ladder geometry

We discuss the occurrence and the stability of charge density plateaux in ladder-like $t-J$ systems (at zero magnetization M=0) for the cases of 2- and 3-leg ladders. Starting from isolated rungs at zero leg coupling, we study the behaviour of plateaux-related phase transitions by means of first order perturbation theory and compare our results with Lanczos diagonalizations for $t-J$ ladders ($N=2\times 8$) with increasing leg couplings. Furthermore we discuss the regimes of rung and leg couplings that should be favoured for the appearance of the charge density plateaux.Comment: 10 pages, 7 figures, RevTex

Formation of clusters in the two dimensional t-J model: The mechanism for phase separation

The emergence of phase separation is investigated in the framework of a 2D t-J model by means of a variational product ansatz, which covers the infinite lattice by two types of L x L clusters. Clusters of the first type are completely occupied with electrons, i.e. they carry maximal charge Q_e=L^2 and total spin 0, and thereby form the antiferromagnetic background. Holes occur in the second type of clusters -- called ``hole clusters''. They carry a charge Q_h<L^2. The charge Q_h and the number N(Q_h) of hole clusters is fixed by minimizing the total energy at given hole density and spin exchange coupling \alpha=J/t. For \alpha not too small (\alpha>0.5) it turns out that hole clusters are occupied with an even number Q_h<L^2 of electrons and carry a total spin 0. For increasing \alpha the charge Q_h(\alpha) of the hole clusters decreases.Some points on the boundary curve can be extracted from Q_h(\alpha).Comment: 11 pages and 3 figure

A numerical study of the formation of magnetisation plateaus in quasi one-dimensional spin-1/2 Heisenberg models

We study the magnetisation process of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with modulated couplings over j=1,2,3 sites. It turns out that the evolution of magnetisation plateaus depends on j and on the wave number q of the modulation according to the rule of Oshikawa, et al. A mapping of two- and three-leg zig-zag ladders on one dimensional systems with modulated couplings yields predictions for the occurence of magnetization plateaus. The latter are tested by numerical computations with the DMRG algorithm.Comment: 7 pages, 10 figures, accepted for publication in Euro. Phys. J.

Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.Comment: 12 pages, REVTEX, 7 figures, submitted to Physical Review

Ferromagnetism in a hard-core boson model

The problem of ferromagnetism -- associated with a ground state with maximal total spin -- is discussed in the framework of a hard-core model, which forbids the occupancy at each site with more than one particle. It is shown that the emergence of ferromagnetism on finite square lattices crucially depends on the statistics of the particles. Fermions (electrons) lead to the well-known instabilities for finite hole densities, whereas for bosons (with spin) ferromagnetism appears to be stable for all hole densities.Comment: 8 pages, 7 figures, RevTex

Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field

The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z spinons, is reconfigured as the physical vacuum for a different species of quasi-particles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasi-particles. For N -> \infty, these collective excitations form a continuum in (q,\omega)-space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor S_{zz}(q,\omega) are calculated directly from the Bethe wave functions for finite N. The resulting lineshape predictions for N -> \infty complement the exact results previously derived via algebraic analysis for the exact 2-spinon part of S_{zz}(q,\omega) in the zero-field limit. They are directly relevant for the interpretation of neutron scattering data measured in nonzero field on quasi-1D antiferromagnetic compounds.Comment: 10 page