Symmetry Spans and Enforced Gaplessness
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915918535196672 |
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| author | Ando, Takamasa Ohmori, Kantaro |
| author_facet | Ando, Takamasa Ohmori, Kantaro |
| contents | Anomaly matching for continuous symmetries has been the primary tool for establishing symmetry enforced gaplessness - the phenomenon where global symmetry alone forces a quantum system to be gapless in the infrared. We introduce a new mechanism based on symmetry spans: configurations in which a global symmetry $\mathcal{E}$ is simultaneously embedded into two larger symmetries, as $\mathcal{D}\hookleftarrow\mathcal{E}\hookrightarrow\mathcal{C}$. Any gapped phase with the full symmetry must, upon restriction to $\mathcal{E}$, arise as the restriction of both a gapped $\mathcal{C}$-symmetric phase and a gapped $\mathcal{D}$-symmetric phase. When no such compatible phase exists, gaplessness is enforced. This mechanism can operate with only discrete and non-anomalous continuous symmetries in the UV, both of which admit well-understood lattice realizations. We construct explicit symmetry spans enforcing gaplessness in 1+1 dimensions, exhibit their realization in conformal field theories, and provide lattice Hamiltonians with the relevant symmetry embeddings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11696 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry Spans and Enforced Gaplessness Ando, Takamasa Ohmori, Kantaro Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Anomaly matching for continuous symmetries has been the primary tool for establishing symmetry enforced gaplessness - the phenomenon where global symmetry alone forces a quantum system to be gapless in the infrared. We introduce a new mechanism based on symmetry spans: configurations in which a global symmetry $\mathcal{E}$ is simultaneously embedded into two larger symmetries, as $\mathcal{D}\hookleftarrow\mathcal{E}\hookrightarrow\mathcal{C}$. Any gapped phase with the full symmetry must, upon restriction to $\mathcal{E}$, arise as the restriction of both a gapped $\mathcal{C}$-symmetric phase and a gapped $\mathcal{D}$-symmetric phase. When no such compatible phase exists, gaplessness is enforced. This mechanism can operate with only discrete and non-anomalous continuous symmetries in the UV, both of which admit well-understood lattice realizations. We construct explicit symmetry spans enforcing gaplessness in 1+1 dimensions, exhibit their realization in conformal field theories, and provide lattice Hamiltonians with the relevant symmetry embeddings. |
| title | Symmetry Spans and Enforced Gaplessness |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.11696 |