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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2406.03983 |
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| _version_ | 1866910475022761984 |
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| author | O'Dea, Nicholas |
| author_facet | O'Dea, Nicholas |
| contents | Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I show by way of several examples that level statistics detect the presence of generalized symmetries that go beyond conventional lattice symmetries and internal symmetries. I consider non-invertible symmetries through the example of Kramers-Wannier duality at an Ising critical point, symmetries with nonlocal generators through the example of a spin-$1$ anisotropic Heisenberg chain, and $q$-deformed symmetries through an example closely related to recent work on $q$-deformed SPT phases. In each case, conventional level statistics detect the generalized symmetries, and these symmetries must be resolved before seeing characteristic level repulsion in non-integrable systems. For the $q$-deformed symmetry, I discovered via level statistics a $q$-deformed generalization of inversion that is interesting in its own right and that may protect $q$-deformed SPT phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03983 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Level statistics detect generalized symmetries O'Dea, Nicholas Statistical Mechanics Quantum Physics Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I show by way of several examples that level statistics detect the presence of generalized symmetries that go beyond conventional lattice symmetries and internal symmetries. I consider non-invertible symmetries through the example of Kramers-Wannier duality at an Ising critical point, symmetries with nonlocal generators through the example of a spin-$1$ anisotropic Heisenberg chain, and $q$-deformed symmetries through an example closely related to recent work on $q$-deformed SPT phases. In each case, conventional level statistics detect the generalized symmetries, and these symmetries must be resolved before seeing characteristic level repulsion in non-integrable systems. For the $q$-deformed symmetry, I discovered via level statistics a $q$-deformed generalization of inversion that is interesting in its own right and that may protect $q$-deformed SPT phases. |
| title | Level statistics detect generalized symmetries |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2406.03983 |