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

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

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

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.

Static and dynamic structure factors in the Haldane phase of the bilinear-biquadratic spin-1

The excitation spectra of the T=0 dynamic structure factors for the spin, dimer, and trimer fluctuation operators as well as for the newly defined center fluctuation operator in the one-dimensional S=1 Heisenberg model wi th isotropic bilinear $(J\cos\theta)$ and biquadratic $(J\sin\theta)$ exchange are investigated via the recursion method for systems with up to N=18 site s over the predicted range, $-\pi/4<\theta\lesssim\pi/4$, of the topologically ordered Haldane phase. The four static and dynamic structure factors probe t he ordering tendencies in the various coupling regimes and the elementary and composite excitations which dominate the T=0 dynamics. At $\theta = \arctan{1/3}$ (VBS point), the dynamically relevant spectra in the invariant subspaces with total spin $S_T = 0,1,2$ are dominated by a branch of magnon states $(S_T = 1)$, by continua of two-magnon scattering states $(S_T = 0,1,2)$, and by discrete branches of two-magnon bound states with positive interaction energy $(S_T = 0,2)$. The dimer and trimer spectra at $q=\pi$ ar e found to consist of single modes with $N$-independent excitation energies $\omega_\lambda^D/|e_0|=5$ and $\omega_\lambda^T/|e_0|=6$, where $e_0=E_0/N$ is the ground-state energy per site. The basic structure of the dynamically relevant excitation spectrum remains the same over a substantial parameter range within the Haldane phase. At the transition to the dimerized phase ($\theta=-\pi/4$), the two-magnon excitations turn into two-spinon excitations.Comment: 12 pages, 4 Postscript figure