电磁对偶与$\mathbb{Z}_2$对称富化阿贝尔格点规范理论
Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory
AI总结：
本文在范畴框架下构造了循环阿贝尔群的$\mathbb{Z}_2$对称富化格点规范模型，实现对称富化拓扑相，并利用$G$-交叉UBFC研究其对称缺陷、任意子凝聚及边界-体对偶，最终给出电磁对偶的显式格点实现。
摘要：
Kitaev的量子双重模型是Dijkgraaf-Witten拓扑量子场论（TQFT）的格点规范理论实现，其受拓扑保护的基态空间在拓扑量子计算和拓扑量子存储中具有广泛应用。我们在范畴框架下研究了循环阿贝尔群的该模型的$\mathbb{Z}_2$对称富化推广，并给出了显式的哈密顿量构造。该模型提供了$\mathbb{Z}_2$对称富化拓扑（SET）相的格点实现。我们详细讨论了该相的范畴对称性，其中电磁（EM）对偶对称性是一个特例。利用$G$-交叉酉编织融合范畴（UBFC）研究了对称缺陷的各个方面。通过确定相应的任意子凝聚，还研究了有能隙边界和边界-体对偶。然后我们仔细构造了这些SET相的电磁对偶的显式格点实现。
英文摘要：
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.
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