Non-Abelian anyons

非阿贝尔任意子

• 批准号: 281472018
• 负责人: Professor Dr. Holger Frahm
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/281472018?language=en
• 关键词: Non; Abelian; anyons

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.

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抑磁体，显示出非常规的量子统计。 这些非Abel任意子的保守拓扑荷被保护，并在量子计算的背景下产生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任意子系统的性质，其构造基于描述融合和编织的基本操作的数学结构。 在微调的相互作用，这些模型可以嵌入到一个家庭的通勤运营商。 我们将开发功能的方法来利用这些可积模型的解决方案，其频谱问题的本地身份。我们对可积任意子链的研究将通过对其不可积变形的研究来补充，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。