论文标题
2D广义量子双模型的边界和域壁理论
Boundary and domain wall theories of 2d generalized quantum double model
论文作者
论文摘要
在这项工作中讨论了基于HOPF代数的2D拓扑订单的广义量子双晶格实现。研究了左模块和右模块构建体。讨论了基于HOPF代数的量子双重表示的色带算子和拓扑激发的分类。为了将模型概括为具有边界和表面缺陷的2D表面，我们提出了边界哈密顿和域壁汉密尔顿的系统结构。间隙边界和域壁背后的代数数据是共同数字代数和双核模块代数。边界和域壁中的拓扑激发通过这些代数上的双模型进行了分类。还讨论了边界构成二元性的带算子实现。最后，通过量子多体态的HOPF张量网络表示，我们在边界和域壁的存在下解决了模型的基态。
The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. The ribbon operators and the classification of topological excitations based on the representations of the quantum double of Hopf algebras are discussed. To generalize the model to a 2d surface with boundaries and surface defects, we present a systematic construction of the boundary Hamiltonian and domain wall Hamiltonian. The algebraic data behind the gapped boundary and domain wall are comodule algebras and bicomodule algebras. The topological excitations in the boundary and domain wall are classified by bimodules over these algebras. The ribbon operator realization of boundary-bulk duality is also discussed. Finally, via the Hopf tensor network representation of the quantum many-body states, we solve the ground state of the model in the presence of the boundary and domain wall.
