Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909689225150464 |
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| author | Kawagoe, Kyle Shirley, Wilbur |
| author_facet | Kawagoe, Kyle Shirley, Wilbur |
| contents | We describe a method for computing the anomaly of any finite unitary symmetry group $G$ acting by finite-depth quantum circuits on a two-dimensional lattice system. The anomaly is characterized by an index valued in the cohomology group $H^4(G,U(1))$, which generalizes the Else-Nayak index for locality preserving symmetries of quantum spin chains. We show that a nontrivial index precludes the existence of a trivially gapped symmetric Hamiltonian; it is also an obstruction to ``onsiteability" of the symmetry action. We illustrate our method via a simple example with $G=\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$. Finally, we provide a diagrammatic interpretation of the anomaly formula which hints at a higher categorical structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems Kawagoe, Kyle Shirley, Wilbur Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics We describe a method for computing the anomaly of any finite unitary symmetry group $G$ acting by finite-depth quantum circuits on a two-dimensional lattice system. The anomaly is characterized by an index valued in the cohomology group $H^4(G,U(1))$, which generalizes the Else-Nayak index for locality preserving symmetries of quantum spin chains. We show that a nontrivial index precludes the existence of a trivially gapped symmetric Hamiltonian; it is also an obstruction to ``onsiteability" of the symmetry action. We illustrate our method via a simple example with $G=\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$. Finally, we provide a diagrammatic interpretation of the anomaly formula which hints at a higher categorical structure. |
| title | Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2507.07430 |