论文标题
拓扑固定点模型的统一图形方法
A unified diagrammatic approach to topological fixed point models
论文作者
论文摘要
我们介绍了一种系统的数学语言来描述固定点模型，并将其应用于物质拓扑阶段。该框架让人联想到状态-AM模型和晶格拓扑量子场理论，但在张量网络方面是形式化和统一的。与现有的张量网络ansatzes相反，用于研究拓扑排序阶段的基础状态，我们形式主义中的张量网络代表了欧几里得时空的离散路径积分。与其他方法相比，这种语言与定义模型的哈密顿定义模型的联系更直接相关，该语言是通过相应的假想时间演变的trotteratization。我们通过简单的例子介绍了我们的形式主义，并通过以最通用的形式以2+1个维度表达已知模型家族，即基于弱的Hopf代数，以2+1个维度表达已知的模型家族。为了阐明我们的形式主义的多功能性，我们还展示了如何描述物质阶段，并为3+1个维度中的拓扑固定点模型提供框架。
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories, but is formalised and unified in terms of tensor networks. In contrast to existing tensor network ansatzes for the study of ground states of topologically ordered phases, the tensor networks in our formalism represent discrete path integrals in Euclidean space-time. This language is more directly related to the Hamiltonian defining the model than other approaches, via a Trotterization of the respective imaginary time evolution. We introduce our formalism by simple examples, and demonstrate its full power by expressing known families of models in 2+1 dimensions in their most general form, namely string-net models and Kitaev quantum doubles based on weak Hopf algebras. To elucidate the versatility of our formalism, we also show how fermionic phases of matter can be described and provide a framework for topological fixed point models in 3+1 dimensions.
