Abstract
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 Λ, are expected to share this feature-entanglement between regions of the vacuum depends upon the UV completion beyond a separation proportional to Λ. 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 ∼e^{-Λd}, 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.
Highlights
Introduction.—Fundamental principles of effective field theories (EFTs) leverage clear separations of energy scales to identify relevant degrees of freedom and to build a systematically improvable hierarchy of local operators
Long-distance physics tends to be insensitive to ultraviolet (UV) modifications incorporated in an EFT through momentum truncations or the “integrating out” of high-energy degrees of freedom
In this Letter, it is shown that the distillable entanglement between two disjoint regions of a massless scalar field is a long-distance observable sensitive to the treatment of the UV degrees of freedom
Summary
Introduction.—Fundamental principles of effective field theories (EFTs) leverage clear separations of energy scales to identify relevant degrees of freedom and to build a systematically improvable hierarchy of local operators. This Letter demonstrates a connection between UV and IR physics with an observation that the entanglement in the vacuum of a simple quantum field, the massless noninteracting scalar field, is sensitive to high-momentum modes at large spatial separations.
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