Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points

Flavio S. Nogueira; Gast\~ao I. Krein; Jeroen van den Brink; Matheus H. Martins Costa

Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points

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arxiv 2211.10238 v2 pith:ZSXNXIAY submitted 2022-11-18 hep-th cond-mat.stat-mechquant-ph

Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points

Matheus H. Martins Costa , Jeroen van den Brink , Flavio S. Nogueira , Gast\~ao I. Krein This is my paper

classification hep-th cond-mat.stat-mechquant-ph

keywords quantumchannelfixedmomentumrenormalizationtheorieswilsonianacting

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We show that the Wilsonian formulation of the renormalization group (RG) defines a quantum channel acting on the momentum-space density matrices of a quantum field theory. This information theoretical property of the RG allows us to derive a remarkable consequence for the vacuum of theories at a fixed point: they have no entanglement between momentum scales. Our result can be understood as deriving from the scale symmetry of such theories and leads to constraints on the form of the ground state and on expectation values of momentum space operators.

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