Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910287769108480 |
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| author | Kapustin, Anton Sopenko, Nikita |
| author_facet | Kapustin, Anton Sopenko, Nikita |
| contents | For any locality-preserving action of a group $G$ on a quantum spin chain one can define an anomaly index taking values in the group cohomology of $G$. The anomaly index is a kinematic quantity, it does not depend on the Hamiltonian. We prove that a nonzero anomaly index prohibits any $G$-invariant Hamiltonian from having $G$-invariant gapped ground states. Lieb-Schultz-Mattis-type theorems are a special case of this result when $G$ involves translations. In the case when the symmetry group $G$ is a Lie group, we define an anomaly index which takes values in the differentiable group cohomology as defined by J.-L. Brylinski and prove a similar result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem Kapustin, Anton Sopenko, Nikita Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory For any locality-preserving action of a group $G$ on a quantum spin chain one can define an anomaly index taking values in the group cohomology of $G$. The anomaly index is a kinematic quantity, it does not depend on the Hamiltonian. We prove that a nonzero anomaly index prohibits any $G$-invariant Hamiltonian from having $G$-invariant gapped ground states. Lieb-Schultz-Mattis-type theorems are a special case of this result when $G$ involves translations. In the case when the symmetry group $G$ is a Lie group, we define an anomaly index which takes values in the differentiable group cohomology as defined by J.-L. Brylinski and prove a similar result. |
| title | Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.02533 |