Inelastic neutron scattering experiments are commonly used to unveil how excitations on Heisenberg spin models play a role in dynamical correlations functions. For a certain class of materials, like CsCoCl
3 or CsCoBr
3 salts, it turns out that their magnetic properties are fairly well approximated by quasi-one dimensional XXZ models, which enjoy the property of quantum integrability. In these instances, one can in principle use their underlying algebraic structure to describe very precisely how excitations, the so-called spinons, participate in dynamical correlations functions. Even though the available theories (either algebraic Bethe ansatz or quantum group approach) provide all the needed physical quantities such as form factors, complete set of eigenstates and spectrum, it is typically a rather daunting task, however, to obtain sufficiently simple analytical expressions for computing Dynamical Structure Factors (DSFs), valuable, e.g., for parameters estimation based on experimental data. This is particularly the case for the longitudinal DSF of the XXZ model, which has eluded a formal mathematical treatment thus far. Using the quantum group approach, we present here an exact and simple expression of the 2-spinon longitudinal DSF and show our results to be consistent with the expected sum rules and the isotropic and Ising antiferromagnet limiting cases.
We consider the XXZ quantum spin chain in its massless, disordered regime at zero field. We derive an exact expression for the two-spinon form factor of by taking a limit of the massive XYZ form factors found by Lashkevich and by Lukyanov and Terras. This result is used to find the two-spinon contribution to the spectral decomposition of the longitudinal structure factor S zz ( k , w ). We find that this contribution provides an accurate approximation to the full structure factor over a wide range of the anisotropy parameter. The asymptotic behaviour of S zz ( k , w ) is computed as the upper and lower w thresholds of the two-spinon ( w , k ) band are approached, and an analysis of the region of validity of this threshold behaviour is performed. Our results reproduce and refine existing threshold behaviour predictions and extend these results to an accurate description throughout the two-spinon continuum.
We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain ( XXZ model) in the gapped antiferromagnetic regime (Δ>1). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the π/2-momentum line, its overall anisotropy dependence, and its contribution to sum rules.