Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field.

The Heisenberg XXZ spin-1/2 chain is considered in the massive antiferromagnetic regime in the presence of a staggered longitudinal magnetic field. The Hamiltonian of the model is characterised by the anisotropy parameter $\Delta<-1$, and by the magnetic field strength h. At zero magnetic field, the model is exactly solvable. In the thermodynamic limit, it has two degenerate vacua and the kinks (which are also called spinons) interpolating between these vacua, as elementary excitations. Application of the staggered magnetic field breaks integrability of the model and induces the long-range attractive potential between two adjacent kinks leading to their confinement into the bound states. The energy spectra of the resulting two-kink bound states is perturbatively calculated in the extreme anisotropic (Ising) limit $\Delta\to-\infty$ to the first order in the inverse anisotropy constant $|\Delta|^{-1}$, and also for generic values of $\Delta<-1$ to the first order in the weak magnetic field h.