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Where multipartite entanglement localizes: The junction law for genuine multientropy

Norihiro Iizuka1,2 and Akihiro Miyata2

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Phys. Rev. D 114, 045021 – Published 24 August, 2026

DOI: https://doi.org/10.1103/jwjk-6tdt

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 multientropy GM2(q) as a diagnostic of genuine 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, GM2(q) exhibits a universal scaling crossover in L/ξ, growing for L≲ξ and saturating to a ξ-dependent constant for L≫ξ, up to O(e−L/ξ) corrections. In sharp contrast, for partitions without a junction, GM2(q) is exponentially suppressed in L/ξ and drops below numerical resolution once L≫ξ. We observe the same pattern for q=3 (tripartite) and 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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Phys. Rev. D 114, 045021– Published 24 August, 2026
  • Received 26 February 2026
  • Accepted 5 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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