A non-semisimple non-invertible symmetry
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912832383090688 |
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| author | Delcamp, Clement Heng, Edmund Yu, Matthew |
| author_facet | Delcamp, Clement Heng, Edmund Yu, Matthew |
| contents | We investigate the action of a non-invertible symmetry on spins chains whose topological lines are labelled by representations of the four-dimensional Taft algebra. The main peculiarity of this symmetry is the existence of junctions between distinct indecomposable lines. Sacrificing Hermiticity, we construct several symmetric, frustration-free, gapped Hamiltonians with real spectra and analyse their ground state subspaces. Our study reveals two intriguing phenomena. First, we identify a smooth path of gapped symmetric Hamiltonians whose ground states transform inequivalently under the symmetry. Second, we find a model where a product state and the so-called W state spontaneously break the symmetry, and propose an explanation for the indistinguishability of these two states in the infinite-volume limit in terms of the symmetry category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-semisimple non-invertible symmetry Delcamp, Clement Heng, Edmund Yu, Matthew Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics We investigate the action of a non-invertible symmetry on spins chains whose topological lines are labelled by representations of the four-dimensional Taft algebra. The main peculiarity of this symmetry is the existence of junctions between distinct indecomposable lines. Sacrificing Hermiticity, we construct several symmetric, frustration-free, gapped Hamiltonians with real spectra and analyse their ground state subspaces. Our study reveals two intriguing phenomena. First, we identify a smooth path of gapped symmetric Hamiltonians whose ground states transform inequivalently under the symmetry. Second, we find a model where a product state and the so-called W state spontaneously break the symmetry, and propose an explanation for the indistinguishability of these two states in the infinite-volume limit in terms of the symmetry category. |
| title | A non-semisimple non-invertible symmetry |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.19635 |