Journal of High Energy Physics

, 2019:219 | Cite as

Entanglement at a scale and renormalization monotones

  • Nima LashkariEmail author
Open Access
Regular Article - Theoretical Physics


We study the information content of the reduced density matrix of a region in quantum field theory that cannot be recovered from its subregion density matrices. We reconstruct the density matrix from its subregions using two approaches: scaling maps and recovery maps. The vacuum of a scale-invariant field theory is the fixed point of both transformations. We define the entanglement of scaling and the entanglement of recovery as measures of entanglement that are intrinsic to the continuum limit. Both measures increase monotonically under the renormalization group flow. This provides a unifying information-theoretic structure underlying the different approaches to the renormalization monotones in various dimensions. Our analysis applies to non-relativistic quantum field theories as well the relativistic ones, however, in relativistic case, the entanglement of scaling can diverge.


Field Theories in Higher Dimensions Nonperturbative Effects Renormalization Group 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.

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