Abstract. We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s = 1 2 Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions z1, . . . , zr of the Bethe ansatz equations, the size of the determinants is of order r ×r. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field.

The Tϭ0 dynamical properties of the one-dimensional ͑1D͒ sϭ 1 2 Heisenberg antiferromagnet in a uniform magnetic field are studied via the Bethe ansatz for cyclic chains of N sites. The ground state at magnetization 0ϽM z ϽN/2, which can be interpreted as a state with 2M z spinons or as a state of N/2ϪM z magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the psinons and antipsinons. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for ͑i͒ the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, ͑ii͒ the calculation of spectral boundaries and densities of states for each continuum, ͑iii͒ the calculation of transition rates between the ground state and the dynamically dominant collective excitations, ͑iv͒ the prediction of line shapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF 3 ,

Abstract. A novel determinantal representation for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s = 1 2 XXZ model is used to calculate transition rates for dynamic spin structure factors in the planar regime. In a first application, high-precision numerical data are presented for lineshapes and band edge singularities of the in-plane (xx) two-spinon dynamic spin structure factor.

As part of a study that investigates the dynamics of the s = 1 2 XXZ model in the planar regime |∆| < 1, we discuss the singular nature of the Bethe ansatz equations for the case ∆ = 0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N = 4096 sites.