论文标题
Kitaev模型中的缺陷和激发
Defects and excitations in the Kitaev model
论文作者
论文摘要
我们使用半简单，有限维的HOPF代数作为缺陷的曲折或2个旋转构建Kitaev模型，作为缺陷数据。该数据是通过将tannaka二元性应用于缺陷的Turaev-Viro拓扑量子场理论来得出的。由此，我们还得出了具有缺陷的Kitaev模型中移动，融合和编织激励的其他条件。我们对Kitaev模型中的激发进行了描述，并表明它们满足了我们从Turaev-Viro拓扑量子量化场理论中得出的条件。分配琐碎的缺陷数据一个人获得了透明的缺陷，我们证明它们可以被删除，从而在没有缺陷的情况下产生Kitaev模型。
We construct a Kitaev model with defects using twists or 2-cocycles of semi-simple, finite-dimensional Hopf algebras as defect data. This data is derived by applying Tannaka duality to Turaev-Viro topological quantum field theories with defects. From this we also derive additional conditions for moving, fusing and braiding excitations in the Kitaev model with defects. We give a description of excitations in the Kitaev model and show that they satisfy conditions we derive from Turaev-Viro topological quantum field theories with defects. Assigning trivial defect data one obtains transparent defects and we show that they can be removed, yielding the Kitaev model without defects.
