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−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≥2. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.
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BibTeX
@misc{kim2026collectivity,
title = {{Collectivity limits quantum entanglement}},
author = {Donghoon Kim and Tomotaka Kuwahara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.36113},
eprint = {2609.36113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36113},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collectivity limits quantum entanglement
AU - Donghoon Kim
AU - Tomotaka Kuwahara
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.36113
UR - https://arxiv.org/abs/2609.36113
AB - 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≥2. Together, these results reveal collectivity as a fundamental mechanism for constraining many-body entanglement alongside spatial locality.
ER -