Non-Abelian anyons

拓扑量子液体中的准粒子，如分数量子霍尔态和某些二维受挫磁体，表现出非常规的量子统计。这些非阿贝尔任意子的守恒拓扑电荷受到保护，并在量子计算的背景下引发了对此类系统的兴趣。在这个项目中，我们计划研究相互作用的多粒子系统的性质，这些系统的结构是基于描述融合和编织基本操作的数学结构。在相互作用的微调之后，这些模型可以嵌入到一个交换算子族中。我们将发展泛函方法来利用这些可积模型中存在的局部恒等式来解决它们的谱问题。我们对可积任意子链的研究将辅以对其不可积变形的研究，以了解非常规边界自由度的出现及其在电子系统中作为拓扑量子杂质的实现。

Quasi particles in topological quantum liquids such as the fractional Quantum Hall states and certain two-dimensional frustrated magnets display unconventional quantum statistics. The conserved topological charge of these non-Abelian anyons is protected and has spawned interest for such systems in the context of quantum computation.In this project we plan to study the properties of interacting many-anyon systems whose construction is based on the mathematical structures describing the fundamental operations of fusion and braiding. Upon fine-tuning of the interactions these models can be embedded into a family of commuting operators. We shall develop functional methods to exploit local identities present in these integrable models for the solution of their spectral problem. Our investigation of integrable anyon chains will be complemented by studies of non-integrable deformations thereof to gain understanding into the emergence of unconventional boundary degrees of freedom and their realization as topological quantum impurities in electronic systems.