Entanglement at a Scale and Renormalization Monotones

Abstract

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.

References in corpus (4)

• Towards a derivation of holographic entanglement entropy
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Markov property of the CFT vacuum and the a-theorem
• Modular Hamiltonians on the null plane and the Markov property of the vacuum state

Cited by in corpus (8)

• Renormalization Group Flow as Optimal Transport
• Aspects of quantum information in finite density field theory
• Probing trihedral corner entanglement for Dirac fermions
• Generalized Entanglement, Charges and Intertwiners
• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Inverted c-functions in thermal states
• Modular zero modes and sewing the states of QFT
• Holographic entanglement entropy inequalities beyond strong subadditivity