Collectivity limits quantum entanglement

Abstract

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 $r^{-\alpha }$ on a $D$-dimensional lattice. For arbitrary bipartitions, we prove that the ground-state entanglement scales at most logarithmically with system size for $\alpha <D/2$ and subextensively for $D/2<\alpha <D$, 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 $D/2<\alpha <(D+1)/2$ and parametrically stronger subvolume bounds for $(D+1)/2<\alpha <D$. We also establish the corresponding optimality results: for arbitrary bipartitions, the logarithmic scaling for $\alpha <D/2$ is optimal and $\alpha =D/2$ marks the optimal threshold for universal logarithmic bounds, while for regular bipartitions the threshold at $\alpha =(D+1)/2$ is likewise optimal for universal polylogarithmic bounds when $D\ge 2$. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.

arXiv comment15 pages, 3 figures; 95 pages Supplementary Material