论文标题
电磁二元性和$ \ MATHBB {Z} _2 $对称性丰富的Abelian晶格仪理论
Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory
论文作者
论文摘要
Kitaev的量子双模型是Dijkgraaf-Witten拓扑量子场理论（TQFT）的晶格规范理论实现，其拓扑受保护的基态空间在拓扑量子计算和拓扑量子记忆中广泛应用。我们研究了$ \ mathbb {z} _2 $对称性在一个分类框架中富含模型的模型的概括，并提出了明显的哈密顿构造。该模型提供了$ \ mathbb {z} _2 $对称富含拓扑（set）阶段的晶格实现。我们详细讨论了该阶段的分类对称性，为此，电磁（EM）二元性对称性是一种特殊情况。使用$ g $的统一编织融合类别（UBFC）研究对称缺陷的各个方面。还可以通过确定相应的Anyon凝结，还研究了间隙边界和边界构成双重性。然后，我们仔细构建了这些设定阶段的EM二元性的明确晶格实现。
Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT), its topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory. We investigate the $\mathbb{Z}_2$ symmetry enriched generalization of the model for the cyclic Abelian group in a categorical framework and present an explicit Hamiltonian construction. This model provides a lattice realization of the $\mathbb{Z}_2$ symmetry enriched topological (SET) phase. We discuss in detail the categorical symmetry of the phase, for which the electric-magnetic (EM) duality symmetry is a special case. The aspects of symmetry defects are investigated using the $G$-crossed unitary braided fusion category (UBFC). By determining the corresponding anyon condensation, the gapped boundaries and boundary-bulk duality are also investigated. Then we carefully construct the explicit lattice realization of EM duality for these SET phases.
