The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q, ) of the one-dimensional sϭ1/2 Heisenberg antiferromagnet at Tϭ0 is evaluated for direct comparison with finite-chain transition rates (Nр28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q, ). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-twospinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q, ) is studied on the basis of finite-size data. ͓S0163-1829͑97͒00517-1͔

No abstract

No abstract

We investigate ground-state energies and magnetization curves in the one-dimensional XXZ model with next-to-nearest neighbor coupling ␣Ͼ0 and anisotropy ⌬ (Ϫ1р⌬р1) at Tϭ0. In between the familiar ferro-and antiferromagnetic phase we find a transition region-called the metamagnetic phase-where the magnetization curve is discontinuous at a critical field B c (␣,⌬). ͓S0163-1829͑98͒01718-4͔

The excitation spectra of the Tϭ0 dynamic structure factors for the spin, dimer, and trimer fluctuation operators as well as for the center fluctuation operator in the one-dimensional Sϭ1 Heisenberg model with isotropic bilinear (J cos ) and biquadratic (J sin ) exchange are investigated via the recursion method for systems with up to Nϭ18 sites over the predicted range, Ϫ/4ϽՇ/4, of the topologically ordered Haldane phase. The four static and dynamic structure factors probe the ordering tendencies in the various coupling regimes and the elementary and composite excitations which dominate the Tϭ0 dynamics. At ϭarctan 1 3 ͑valence-bond solid point͒, the dynamically relevant spectra in the invariant subspaces with total spin S T ϭ0,1,2 are dominated by a branch of magnon states (S T ϭ1), by continua of two-magnon scattering states (S T ϭ0,1,2), and by discrete branches of two-magnon bound states with positive interaction energy (S T ϭ0,2). The dimer and trimer spectra at qϭ are found to consist of single modes with N-independent excitation energies D /͉e 0 ͉ϭ5 and T /͉e 0 ͉ϭ6, where e 0 ϭE 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 (ϭϪ/4), the two-magnon excitations turn into two-spinon excitations. ͓S0163-1829͑98͒00233-1͔

In the presence of a uniform field the one-dimensional spin-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.

We present results on the magnetization curves for the antiferromagnetic Heisenberg model in one and two dimensions.

No abstract