摘要
<p>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 Renyi-2 genuine multientropy GM(2)((q)) as a diagnostic of genuine q-partite entanglement, we establish this behavior in (2 ) 1)-dimensional gapped free-fermion lattices with correlation length xi. For partitions with a single junction, GM(2)((q)) exhibits a universal scaling crossover in L=xi, growing for L less than or similar to xi and saturating to a xi-dependent constant for L >> xi, up to Oe-L=xi) corrections. In sharp contrast, for partitions without a junction, GM(2)((q)) is exponentially suppressed in L=xi and drops below numerical resolution once L >> xi. 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.</p>