Anomaly-free symmetries with obstructions to gauging and onsiteability
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909710001635328 |
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| author | Shirley, Wilbur Zhang, Carolyn Ji, Wenjie Levin, Michael |
| author_facet | Shirley, Wilbur Zhang, Carolyn Ji, Wenjie Levin, Michael |
| contents | We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields or disentangled to a tensor product of on-site operators. These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states. We show that symmetries of this kind are characterized by an index $[ω]\in H^2(G,\mathbb{Q}_+)$, where $\mathbb{Q}_+$ is the multiplicative group of rational numbers labeling one-dimensional quantum cellular automata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomaly-free symmetries with obstructions to gauging and onsiteability Shirley, Wilbur Zhang, Carolyn Ji, Wenjie Levin, Michael Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields or disentangled to a tensor product of on-site operators. These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states. We show that symmetries of this kind are characterized by an index $[ω]\in H^2(G,\mathbb{Q}_+)$, where $\mathbb{Q}_+$ is the multiplicative group of rational numbers labeling one-dimensional quantum cellular automata. |
| title | Anomaly-free symmetries with obstructions to gauging and onsiteability |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2507.21267 |