Non-invertible SPT, gauging and symmetry fractionalization
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917674683990016 |
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| author | Li, Yabo Litvinov, Mikhail |
| author_facet | Li, Yabo Litvinov, Mikhail |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-invertible SPT, gauging and symmetry fractionalization Li, Yabo Litvinov, Mikhail Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics 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. |
| title | Non-invertible SPT, gauging and symmetry fractionalization |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.15951 |