We consider a one-dimensional Ising-like fully anisotropic
S=21 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain-wall excitations in the presence of a staggered magnetic field,
hx, along the transverse direction. We obtain dynamical spin-correlation functions along the magnetic field, ${S}^{xx}(q,\ensuremath{\omega})$, and perpendicular to it, ${S}^{yy}(q,\ensuremath{\omega})$. It is shown that the line shapes of ${S}^{xx}(q,\ensuremath{\omega})$ and ${S}^{yy}(q,\ensuremath{\omega})$ are purely symmetric at the zone boundary, $q=\frac{\ensuremath{\pi}}{2}$. It is observed in ${S}^{xx}(q,\ensuremath{\omega})$ for $\ensuremath{\pi}/2<q<\ensuremath{\pi}$ that the spectral weight moves toward high-energy side with the increase in
hx. We discuss the relevance of this model to explain the spin dynamics of
CsCoCl3 in presence of weak staggered field.
We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions. To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in one dimension. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from one-dimensional (1D) to 2D physics.