Confinement in quasi one-dimensional magnetically ordered quantum spin systems

限制意味着某些粒子不能孤立存在，而必须形成束缚态。这一现象最著名的例子是强子中夸克的禁闭。但是在凝聚态系统中也可以观察到禁闭。一个最重要的例子是自旋链化合物中自旋子的限制（=拓扑或扭结激发），其中扭结之间的线性吸引势是由相邻磁链之间的弱耦合引起的。最近在几种铁磁和反铁磁化合物的中子散射和太赫兹光谱实验中观察到了这种类型的扭结约束。拟议的研究项目的主要目标是进行分析的实验相关的量，包括两个扭结束缚态的能谱和动力学结构因子的第一主计算。我们感兴趣的主要课题将是XXZ自旋1/2链，是一个现实的一维量子反铁磁体模型。在这个模型中，如果反铁磁质量相受到一个模拟与相邻链平均相互作用的可积性破坏交错磁场$h>0$的扰动，则会发生扭结的限制。在$h=0$的模型的可积性将使人们有可能通过一个小-$h$微扰分析的基础上的Bethe-Salpeter方程的约束现象进行研究。

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.