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 suppress collective quantum fluctuations while retaining a finite overall interaction scale. 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 show that collective suppression can be propagated to successively larger length scales through a renormalization-group construction. As a result, we prove that the entanglement bound improves to polylogarithmic scaling for $D/2<α<(D+1)/2$, and remains parametrically stronger than the arbitrary-bipartition bound for $(D+1)/2<α<D$. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.