Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory

• URL: http://arxiv.org/abs/2201.12361v3
• Date: Fri, 24 May 2024 12:20:13 GMT
• Title: Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory
• Authors: Zhian Jia, Dagomir Kaszlikowski, Sheng Tan,
• Abstract summary: Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT) Topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory.
• Score: 2.206623168926072
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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