Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain

The infinite Heisenberg XXZ spin-(1/2) chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic field h induces a long-range attractive potential between two adjacent spinons leading to their confinement into 'meson' bound states. Exploiting the integrability of the XXZ model in the deconfined phase h = 0, we perform perturbative calculations of the energy spectra of the two-spinon bound states in the weak confinement regime at h \to +0, using the strength of the staggered magnetic field h as a small parameter. Both transverse and longitudinal dynamical structure factors of the local spin operators are calculated as well in the two-spinon approximation in the weak confinement regime to the leading order in h.