The Large-Scale Structure of Entanglement in Quantum Many-body Systems

• URL: http://arxiv.org/abs/2503.03833v2
• Date: Tue, 08 Apr 2025 13:20:51 GMT
• Title: The Large-Scale Structure of Entanglement in Quantum Many-body Systems
• Authors: Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming,
• Abstract summary: We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems.<n>In particular, we show that every gapped phase of matter, even the trivial one, in $Dgeq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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