Where Multipartite Entanglement Localizes: The Junction Law for Genuine Multi-Entropy

• URL: http://arxiv.org/abs/2602.16331v1
• Date: Wed, 18 Feb 2026 10:12:06 GMT
• Title: Where Multipartite Entanglement Localizes: The Junction Law for Genuine Multi-Entropy
• Authors: Norihiro Iizuka, Akihiro Miyata,
• Abstract summary: We find a "junction law" for genuine multipartite entanglement in gapped local systems.<n>In this gapped free-fermion setting genuine multipartite entanglement is localized within a correlation-length neighborhood of junctions.
• Score: 2.477977081568645
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We uncover a "junction law" for genuine multipartite entanglement, suggesting that in gapped local systems multipartite entanglement is controlled and effectively localized near junctions where subsystem boundaries meet. Using the Rényi-2 genuine multi-entropy $\mathrm{GM}^{(\mathtt{q})}_2$ as a diagnostic of genuine $\mathtt{q}$-partite entanglement, we establish this behavior in $(2+1)$-dimensional gapped free-fermion lattices with correlation length $ξ$. For partitions with a single junction, $\mathrm{GM}^{(\mathtt{q})}_2$ exhibits a universal scaling crossover in $L/ξ$, growing for $L\llξ$ and saturating to a $ξ$-dependent constant for $L\ggξ$, up to $\mathcal{O}(e^{-L/ξ})$ corrections. In sharp contrast, for partitions without a junction, $\mathrm{GM}^{(\mathtt{q})}_2$ is exponentially suppressed in $L/ξ$ and drops below numerical resolution once $L\ggξ$. We observe the same pattern for $\mathtt{q}=3$ (tripartite) and $\mathtt{q}=4$ (quadripartite) cases, and further corroborate this localization by translating the junction at fixed system size. We also provide a geometric explanation of the junction law in holography. Altogether, these results show that in this gapped free-fermion setting genuine multipartite entanglement is localized within a correlation-length neighborhood of junctions.

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