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

Disjoint regions of the latticized, massless scalar field vacuum become separable at large distances beyond the entanglement sphere, a distance that extends to infinity in the continuum limit. Through numerical calculations in one-, two- and three-dimensions, the radius of an entanglement sphere is found to be determined by the highest momentum mode of the field supported across the diameter, $d$, of two identical regions. As a result, the long-distance behavior of the entanglement is determined by the short-distance structure of the field. Effective field theories (EFTs), describing a system up to a given momentum scale $\Lambda$, are expected to share this feature, with regions of the EFT vacuum separable (or dependent on the UV-completion) beyond a distance proportional to $\Lambda$. The smallest non-zero value of the entanglement negativity supported by the field at large distances is conjectured to be $\mathcal{N}_{{ {\cal N}\hskip-0.55em /}} \sim e^{-\Lambda d}$, independent of the number of spatial dimensions. This phenomenon may be manifest in perturbative QCD processes.