多体纠缠的局部化：真正的多熵的连接定律
Where Multipartite Entanglement Localizes: The Junction Law for Genuine Multi-Entropy
AI总结：
该研究揭示了在有能隙的自由费米子系统中，真正的多体纠缠在连接处被局部化，并通过多熵诊断和几何解释验证了这一现象。
摘要：
我们揭示了真正的多体纠缠的'连接定律'，表明在有能隙的本地系统中，多体纠缠被控制并有效局部化在子系统边界交汇的连接处。使用Rényi-2真正的多熵GM^(q)₂作为真正的q-体纠缠的诊断工具，我们在(2+1)维有能隙的自由费米子晶格中建立了这种行为，其关联长度为ξ。对于具有单个连接的划分，GM^(q)₂表现出在L/ξ上的普遍尺度交叉，当L<<ξ时增长，当L>>ξ时趋于ξ依赖的常数，误差不超过O(e^{-L/ξ})。相反，对于没有连接的划分，GM^(q)₂在L/ξ上呈指数衰减，当L>>ξ时低于数值分辨率。我们观察到q=3（三体）和q=4（四体）情况下的相同模式，并通过在固定系统大小下移动连接来进一步证实这种局部化。我们还提供了在引力学中的几何解释。这些结果表明，在这种有能隙的自由费米子设置中，真正的多体纠缠被局部化在关联长度范围内的连接处。
英文摘要：
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.
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