Noninvertible Symmetry-Enriched Quantum Critical Point
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912136609923072 |
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| author | Li, Linhao Huang, Rui-Zhen Cao, Weiguang |
| author_facet | Li, Linhao Huang, Rui-Zhen Cao, Weiguang |
| contents | Noninvertible symmetry generalizes traditional group symmetries, advancing our understanding of quantum matter, especially one-dimensional gapped quantum systems. In critical lattice models, it is usually realized as emergent symmetries in the corresponding low-energy conformal field theories. In this work, we study critical lattice models with the noninvertible Rep($D_8$) symmetry in one dimension. This leads us to a new class of quantum critical points (QCP), noninvertible symmetry-enriched QCPs, as a generalization of known group symmetry-enriched QCPs. They are realized as phase transitions between one noninvertible symmetry-protected topological (SPT) phase and another different one or spontaneous symmetry breaking (SSB) phase. We identify their low-energy properties and topological features through the Kennedy-Tasaki (KT) duality transformation. We argue that distinct noninvertible symmetry-enriched QCPs can not be smoothly connected without a phase transition or a multi-critical point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noninvertible Symmetry-Enriched Quantum Critical Point Li, Linhao Huang, Rui-Zhen Cao, Weiguang Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics Noninvertible symmetry generalizes traditional group symmetries, advancing our understanding of quantum matter, especially one-dimensional gapped quantum systems. In critical lattice models, it is usually realized as emergent symmetries in the corresponding low-energy conformal field theories. In this work, we study critical lattice models with the noninvertible Rep($D_8$) symmetry in one dimension. This leads us to a new class of quantum critical points (QCP), noninvertible symmetry-enriched QCPs, as a generalization of known group symmetry-enriched QCPs. They are realized as phase transitions between one noninvertible symmetry-protected topological (SPT) phase and another different one or spontaneous symmetry breaking (SSB) phase. We identify their low-energy properties and topological features through the Kennedy-Tasaki (KT) duality transformation. We argue that distinct noninvertible symmetry-enriched QCPs can not be smoothly connected without a phase transition or a multi-critical point. |
| title | Noninvertible Symmetry-Enriched Quantum Critical Point |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2411.19034 |