Non-invertible SPT, gauging and symmetry fractionalization

• URL: http://arxiv.org/abs/2405.15951v1
• Date: Fri, 24 May 2024 21:35:55 GMT
• Title: Non-invertible SPT, gauging and symmetry fractionalization
• Authors: Yabo Li, Mikhail Litvinov,
• Abstract summary: We construct the lattice models for the phases of all the symmetries in the Rep($Q_8$) duality web. We show that these interplay can be explained using the symmetry fractionalization in the 2+1d bulk SET.
• Score: 2.541410020898643
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explicitly realize the Rep($Q_8$) non-invertible symmetry-protected topological (SPT) state as a 1+1d cluster state on a tensor product Hilbert space of qubits. Using the Kramers-Wannier operator, we construct the lattice models for the phases of all the symmetries in the Rep($Q_8$) duality web. We further show that we can construct a class of lattice models with Rep($G$) symmetry including non-invertible SPT phases if they have a dual anomalous abelian symmetry. Upon dualizing, there is a rich interplay between onsite symmetries, non-onsite symmetries, non-abelian symmetries, and non-invertible symmetries. We show that these interplay can be explained using the symmetry fractionalization in the 2+1d bulk SET.

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