Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.
Recent low-temperature inelastic neutron scattering data on the quasi-one-dimensional (1D) Heisenberg-Ising antiferromagnet (AFM) CsCo
Cl3 call for new theoretical efforts, for the available theories fail to explain the observed line shapes. In this paper we initiate a detailed study of the dynamical properties of the 1D spin-\textonehalf{} anisotropic
XYZ AFM with emphasis on the dynamic structure factor ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at
T=0. The structure of ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ is determined by the combined effects of the density of states and the matrix elements. Both effects are discussed for selected cases: the
XY-Heisenberg AFM (planar system), the Heisenberg-Ising AFM (uniaxial system), and the
XY-Ising AFM (biaxial system). The exact solution for ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ of the
XY-Ising AFM has already many features in common with the experimental data on CsCo
Cl3. It is an ideal starting point for a perturbation approach to the Heisenberg-Ising AFM.