发表机构
RIKEN Center for Quantum Computing (RQC); RIKEN Pioneering Research Institute (PRI)（理化学研究所量子计算中心; 理化学研究所先锋研究本部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在非局域相互作用下，集体性可像空间局域性一样约束多体纠缠，对幂律相互作用哈密顿量给出基态纠缠的严格上界。
AI 中文摘要
理解什么限制了多体量子纠缠是物理学中的一个核心问题。空间局域性长期以来提供了一个基本机制：一个区域与其补集之间的关联必须通过一个小的空间界面来传递，从而约束了它们的纠缠。在这里，我们表明，即使相互作用是强非局域的，通过集体性，对纠缠的普适约束也可以持续存在：许多弱相互作用抑制了集体量子涨落，同时保留了有限的整体相互作用尺度。我们在D维晶格上，对具有Kac归一化幂律相互作用$r^{-\alpha}$的一般带隙哈密顿量严格建立了这一机制。对于任意二分，我们证明了当$\alpha<D/2$时，基态纠缠随系统大小最多呈对数增长，当$D/2<\alpha<D$时，呈次广延增长，这是由于单个位点周围的集体涨落受到抑制。对于具有余维一边界且空间规则的二分，我们表明通过重整化群构造，集体抑制可以传播到逐渐更大的长度尺度。因此，我们证明了当$D/2<\alpha<(D+1)/2$时，纠缠界改进为多对数标度，并且当$(D+1)/2<\alpha<D$时，仍参数性地强于任意二分界。这些结果共同揭示了集体性是与空间局域性并列的约束多体纠缠的基本机制。
英文摘要
Understanding what limits many-body quantum entanglement is a central problem in physics. Spatial locality has long provided a fundamental mechanism: correlations between a region and its complement must be mediated through a small spatial interface, thereby constraining their entanglement. Here we show that universal constraints on entanglement can persist even when interactions are strongly nonlocal, through collectivity: many weak interactions generate fluctuations controlled by their square-summed, rather than total, strength. We establish this mechanism rigorously for generic gapped Hamiltonians with Kac-normalized power-law interactions $r^{-α}$ on a $D$-dimensional lattice. For arbitrary bipartitions, we prove that the ground-state entanglement scales at most logarithmically with system size for $α<D/2$ and subextensively for $D/2<α<D$, due to suppressed collective fluctuations around individual sites. For spatially regular bipartitions with codimension-one boundaries, we use a renormalization-group construction to extend this suppression to larger length scales, yielding polylogarithmic scaling for $D/2 < α< (D+1) / 2$ and parametrically stronger subvolume bounds for $(D+1)/2<α<D$. We also establish the corresponding optimality results: for arbitrary bipartitions, the logarithmic scaling for $α<D/2$ is optimal and $α=D/2$ marks the optimal threshold for universal logarithmic bounds, while for regular bipartitions the threshold at $α=(D+1)/2$ is likewise optimal for universal polylogarithmic bounds when $D\ge2$. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.
Comments15 pages, 3 figures; 95 pages Supplementary Material
