Confinement in quasi one-dimensional magnetically ordered quantum spin systems

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Confinement means that certain particles cannot exist in isolation, but must form bound states. The most famous example for this phenomenon is the confinement of quarks in hadrons. But confinement can also be observed in condensed matter systems. A most important example here is the confinement of spinons (= topological or kink excitations) in spin-chain compounds in which a linear attractive potential between the kinks is induced by a weak coupling between neighbouring magnetic chains. Kink confinement of this type was recently observed in neutron-scattering and terahertz-spectroscopy experiments in several ferro- and antiferromagnetic compounds. The main objective of the proposed research project is to perform analytic first-principal calculations of the experimentally relevant quantities, including the energy spectrum of the two-kink bound states and the dynamical structure factor. Our primary subject of interest will be the XXZ spin-1/2 chain, being a realistic model of a one-dimensional quantum anti-ferromagnet. Confinement of kinks takes place in the antiferromagnetic massive phase of this model, if it is perturbed by an integrability-breaking staggered magnetic field $h>0$ simulating the mean interaction with neighbouring chains. The integrability of the model at $h=0$ will make it possible to study the confinement phenomenon by means of a small-$h$ perturbative analysis based on the Bethe-Salpeter equation.