摘要
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.