Entanglement Spheres and a UV-IR connection in Effective Field Theories

We show that long-distance quantum correlations probe short-distance physics. Two disjoint regions of the latticized, massless scalar field vacuum are numerically demonstrated to become separable at distances beyond the negativity sphere, which extends to infinity in the continuum limit. The size of this quantum coherent volume is determined by the highest momentum mode supported in the identical regions, each of diameter $d$. More generally, effective field theories (EFTs), describing a system up to a given momentum scale $\Lambda$, are expected to share this feature -- entanglement between regions of the vacuum depends upon the UV-completion beyond a separation proportional to $\Lambda$. Through calculations extended to three-dimensions, the magnitude of the negativity at which entanglement becomes sensitive to UV physics in an EFT (lattice or otherwise) is conjectured to scale as $\sim e^{-\Lambda d}$, independent of the number of spatial dimensions. It is concluded that two-region vacuum entanglement at increasing separations depends upon the structure of the theory at increasing momentum scales. This phenomenon may be manifest in perturbative QCD processes.