论文标题
Kitaev模型和Bicomodule代数的缺陷
Defects in Kitaev models and bicomodule algebras
论文作者
论文摘要
We construct a Kitaev model, consisting of a Hamiltonian which is the sum of commuting local projectors, for surfaces with boundaries and defects of dimension 0 and 1. More specifically, we show that one can consider cell decompositions of surfaces whose 2-cells are labeled by semisimple Hopf algebras and 1-cells are labeled by semisimple bicomodule algebras.我们引入了一个代数，其表示为0细胞，并在没有缺陷的情况下将HOPF代数的Drinfeld双重降低。通过这种方式，我们将标准Kitaev模型基础的代数结构推广而没有缺陷或边界，其中所有1个单元和2个细胞都由单个Hopf代数标记，其中点缺陷被其Drinfeld double的表示形式标记。在标准案例中，通勤本地投影仪是使用半hopf代数的HAAR积分构建的。我们在本文中获得的一个中心见解是，在存在缺陷和边界的情况下，HAAR积分的合适概括是由唯一的对称性可分离性对半模拟（BI-）综合代数给出的。
We construct a Kitaev model, consisting of a Hamiltonian which is the sum of commuting local projectors, for surfaces with boundaries and defects of dimension 0 and 1. More specifically, we show that one can consider cell decompositions of surfaces whose 2-cells are labeled by semisimple Hopf algebras and 1-cells are labeled by semisimple bicomodule algebras. We introduce an algebra whose representations label the 0-cells and which reduces to the Drinfeld double of a Hopf algebra in the absence of defects. In this way we generalize the algebraic structure underlying the standard Kitaev model without defects or boundaries, where all 1-cells and 2-cells are labeled by a single Hopf algebra and where point defects are labeled by representations of its Drinfeld double. In the standard case, commuting local projectors are constructed using the Haar integral for semisimple Hopf algebras. A central insight we gain in this paper is that in the presence of defects and boundaries, the suitable generalization of the Haar integral is given by the unique symmetric separability idempotent for a semisimple (bi-)comodule algebra.
