Geometric additivity of modular commutator for multipartite entanglement
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915290044956672 |
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| author | Park, Sung-Min Kim, Isaac H. Moon, Eun-Gook |
| author_facet | Park, Sung-Min Kim, Isaac H. Moon, Eun-Gook |
| contents | A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function. Here, we unveil novel geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We obtain the geometric additivity of a modular commutator, indicating that modular commutator for a multipartite system may be an integer multiple of the one for tripartite systems. Using our additivity formula, we also derive a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories. We further illustrate this geometric additivity for both bulk and edge subsystems using numerical calculations of the Haldane and $π$-flux models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric additivity of modular commutator for multipartite entanglement Park, Sung-Min Kim, Isaac H. Moon, Eun-Gook Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function. Here, we unveil novel geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We obtain the geometric additivity of a modular commutator, indicating that modular commutator for a multipartite system may be an integer multiple of the one for tripartite systems. Using our additivity formula, we also derive a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories. We further illustrate this geometric additivity for both bulk and edge subsystems using numerical calculations of the Haldane and $π$-flux models. |
| title | Geometric additivity of modular commutator for multipartite entanglement |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.11130 |