Identification of gapless phases by a twisting operator
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912624778674176 |
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| author | Su, Hang Zhang, Tengzhou Yao, Yuan Furusaki, Akira |
| author_facet | Su, Hang Zhang, Tengzhou Yao, Yuan Furusaki, Akira |
| contents | We propose a general necessary condition for a spin chain with SO(3) spin-rotation symmetry to be gapped. Specifically, we prove that the ground state(s) of an SO(3)-symmetric gapped spin chain must be spin singlet(s), and the expectation value of a twisting operator asymptotically approaches unity in the thermodynamic limit, where finite-size corrections are inversely proportional to the system size. This theorem provides (i) supporting evidence for various conjectured gapped phases, and (ii) a sufficient criterion for identifying gapless spin chains. We verify our theorem by numerical simulations for a variety of spin models and show that it offers a novel efficient way to identify gapless phases in spin chains with spin-rotation symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identification of gapless phases by a twisting operator Su, Hang Zhang, Tengzhou Yao, Yuan Furusaki, Akira Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics We propose a general necessary condition for a spin chain with SO(3) spin-rotation symmetry to be gapped. Specifically, we prove that the ground state(s) of an SO(3)-symmetric gapped spin chain must be spin singlet(s), and the expectation value of a twisting operator asymptotically approaches unity in the thermodynamic limit, where finite-size corrections are inversely proportional to the system size. This theorem provides (i) supporting evidence for various conjectured gapped phases, and (ii) a sufficient criterion for identifying gapless spin chains. We verify our theorem by numerical simulations for a variety of spin models and show that it offers a novel efficient way to identify gapless phases in spin chains with spin-rotation symmetry. |
| title | Identification of gapless phases by a twisting operator |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.02496 |