论文标题
（2+1）维度的交换对称性的融合结构
Fusion Structure from Exchange Symmetry in (2+1)-Dimensions
论文作者
论文摘要
直到最近，还缺乏从某些基本的物理原理中仔细推导任何人的融合结构。在[Shi等人，Ann。 Phys。，418（2020）]，作者从猜想形式的纠缠区域法开始，用于2D Gapped Systems。在这项工作中，我们从交换对称性的原理开始，并确定与单一色带融合类别接触所需的其他假设的最小处方，作为用于建模Anyons的适当代数框架。假设2D准粒子是空间定位的，我们将构建一个函子，从彩色辫子群体到有限维的希尔伯特空间的类别。使用此函子，我们构建了交换对称性的精确概念，使我们能够恢复Anyons的核心融合属性。特别是，给定$ n $ quasiparticles的系统，我们表明某个$ n $ -braid $β_{n} $的动作唯一指定其超选择扇区。然后，我们概述了在编织$ 6J $融合系统的通常环境中，Anyons的编织和融合结构。通过提出[A.的双重性公理基塔夫，安。 Phys。，321（1）（2006）]，假设有许多不同的拓扑费用，我们到达了色带类别的框架。
Until recently, a careful derivation of the fusion structure of anyons from some underlying physical principles has been lacking. In [Shi et al., Ann. Phys., 418 (2020)], the authors achieved this goal by starting from a conjectured form of entanglement area law for 2D gapped systems. In this work, we instead start with the principle of exchange symmetry, and determine the minimal prescription of additional postulates needed to make contact with unitary ribbon fusion categories as the appropriate algebraic framework for modelling anyons. Assuming that 2D quasiparticles are spatially localised, we build a functor from the coloured braid groupoid to the category of finite-dimensional Hilbert spaces. Using this functor, we construct a precise notion of exchange symmetry, allowing us to recover the core fusion properties of anyons. In particular, given a system of $n$ quasiparticles, we show that the action of a certain $n$-braid $β_{n}$ uniquely specifies its superselection sectors. We then provide an overview of the braiding and fusion structure of anyons in the usual setting of braided $6j$ fusion systems. By positing the duality axiom of [A. Kitaev, Ann. Phys., 321(1) (2006)] and assuming that there are finitely many distinct topological charges, we arrive at the framework of ribbon categories.
