The Large-Scale Structure of Entanglement in Quantum Many-body Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916678093242368 |
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| author | van Luijk, Lauritz Stottmeister, Alexander Wilming, Henrik |
| author_facet | van Luijk, Lauritz Stottmeister, Alexander Wilming, Henrik |
| contents | We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems -- similar to how phase transitions only sharply emerge in the thermodynamic limit. The resulting operational entanglement properties are in one-to-one correspondence with abstract properties of the local observable algebras that emerge in the thermodynamic limit. These properties are insensitive to finite perturbations and hence describe the $\textit{large-scale structure of entanglement}$ of many-body systems. We formulate and discuss the emerging structures and open questions, both for gapped and gapless many-body systems. In particular, we show that every gapped phase of matter, even the trivial one, in $D\geq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement. Conversely, we conjecture the existence of topological phases of matter, where all representatives have the strongest form of entanglement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Large-Scale Structure of Entanglement in Quantum Many-body Systems van Luijk, Lauritz Stottmeister, Alexander Wilming, Henrik Quantum Physics Strongly Correlated Electrons Mathematical Physics Operator Algebras We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems -- similar to how phase transitions only sharply emerge in the thermodynamic limit. The resulting operational entanglement properties are in one-to-one correspondence with abstract properties of the local observable algebras that emerge in the thermodynamic limit. These properties are insensitive to finite perturbations and hence describe the $\textit{large-scale structure of entanglement}$ of many-body systems. We formulate and discuss the emerging structures and open questions, both for gapped and gapless many-body systems. In particular, we show that every gapped phase of matter, even the trivial one, in $D\geq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement. Conversely, we conjecture the existence of topological phases of matter, where all representatives have the strongest form of entanglement. |
| title | The Large-Scale Structure of Entanglement in Quantum Many-body Systems |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2503.03833 |