2024/12/29 by Xinping Yang, Meng, Chenqi, Yang, Xinping +4 · 4 citations
Physics and Astronomy · #Atomic and Subatomic Physics Research #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2412.20546
openalex publication_date 2024/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate (1+1)d symmetry-protected topological (SPT) phases with fusion category symmetries. We emphasize that the UV description of an anomaly-free fusion category symmetry must include the fiber functor, giving rise to a local symmetry action, a charge category and a trivial phase. We construct an ``onsite'' matrix-product-operator (MPO) version of the Hopf algebra symmetry operators in a lattice model with tensor-product Hilbert space. In particular, we propose a systematic framework for classifying and constructing SPTs with non-invertible symmetries. An SPT phase corresponds to a Q-system in the charge category, such that the Q-system becomes a matrix algebra when the symmetry is forgotten. As an example, we provide an explicit microscopic realization of all three Rep^†(D8) SPT phases, including a trivial phase, and further demonstrate the S3-duality among these three SPT phases.