Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910503527251968 |
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| author | Mana, Aswin Parayil Li, Yabo Sukeno, Hiroki Wei, Tzu-Chieh |
| author_facet | Mana, Aswin Parayil Li, Yabo Sukeno, Hiroki Wei, Tzu-Chieh |
| contents | We give an explicit operator representation (via a sequential circuit and projection to symmetry subspaces) of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models generalizing the construction in the 1D transverse-field Ising model. Using the Kramers-Wannier duality operator, we also construct the Kennedy-Tasaki transformation that maps subsystem symmetry-protected topological phases to spontaneous subsystem symmetry breaking phases, where the symmetry group for the former is either $\mathbb{Z}_2\times\mathbb{Z}_2$ or $\mathbb{Z}_2$. This generalizes the recently proposed picture of one-dimensional Kennedy-Tasaki transformation as a composition of manipulations involving gauging and stacking symmetry-protected topological phases to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension Mana, Aswin Parayil Li, Yabo Sukeno, Hiroki Wei, Tzu-Chieh Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We give an explicit operator representation (via a sequential circuit and projection to symmetry subspaces) of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models generalizing the construction in the 1D transverse-field Ising model. Using the Kramers-Wannier duality operator, we also construct the Kennedy-Tasaki transformation that maps subsystem symmetry-protected topological phases to spontaneous subsystem symmetry breaking phases, where the symmetry group for the former is either $\mathbb{Z}_2\times\mathbb{Z}_2$ or $\mathbb{Z}_2$. This generalizes the recently proposed picture of one-dimensional Kennedy-Tasaki transformation as a composition of manipulations involving gauging and stacking symmetry-protected topological phases to higher dimensions. |
| title | Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2402.09520 |