Topological Orders from Reflection Positive Frustration-free Hamiltonians
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914174391549952 |
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| author | Liu, Zhengwei Zhao, Zishuo |
| author_facet | Liu, Zhengwei Zhao, Zishuo |
| contents | We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the local topological quantum order (LTQO) condition of ground states on a disk holds if and only if the ground state on the sphere is non-degenerate. Furthermore, we show that the Osterwalder-Schrader reconstruction produces the boundary local net of operator algebras from the local ground states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Orders from Reflection Positive Frustration-free Hamiltonians Liu, Zhengwei Zhao, Zishuo Mathematical Physics Strongly Correlated Electrons Quantum Physics 81R15, 81T25 (Primary) 81T08, 81V27, 18M20 (Secondary) We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the local topological quantum order (LTQO) condition of ground states on a disk holds if and only if the ground state on the sphere is non-degenerate. Furthermore, we show that the Osterwalder-Schrader reconstruction produces the boundary local net of operator algebras from the local ground states. |
| title | Topological Orders from Reflection Positive Frustration-free Hamiltonians |
| topic | Mathematical Physics Strongly Correlated Electrons Quantum Physics 81R15, 81T25 (Primary) 81T08, 81V27, 18M20 (Secondary) |
| url | https://arxiv.org/abs/2510.20662 |