%0 Journal Article %1 PhysRevD.107.125014 %A Martins Costa, Matheus H. %A van den Brink, Jeroen %A Nogueira, Flavio S. %A Krein, Gastão I. %D 2023 %I American Physical Society %J Phys. Rev. D %K a b %N 12 %P 125014 %R 10.1103/PhysRevD.107.125014 %T Wilsonian renormalization as a quantum channel and the separability of fixed points %U https://link.aps.org/doi/10.1103/PhysRevD.107.125014 %V 107 %X 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.

@article{PhysRevD.107.125014, abstract = {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.}, added-at = {2023-06-21T14:21:35.000+0200}, author = {Martins Costa, Matheus H. and van den Brink, Jeroen and Nogueira, Flavio S. and Krein, Gastão I.}, biburl = {https://www.bibsonomy.org/bibtex/28a96be247acdd76ad3254a85d4e0cf7f/ctqmat}, day = 15, description = {Wilsonian renormalization as a quantum channel and the separability of fixed points}, doi = {10.1103/PhysRevD.107.125014}, interhash = {52027bb0f3088079091968997e0ae045}, intrahash = {8a96be247acdd76ad3254a85d4e0cf7f}, journal = {Phys. Rev. D}, keywords = {a b}, month = {06}, number = 12, numpages = {7}, pages = 125014, publisher = {American Physical Society}, timestamp = {2023-06-21T14:23:43.000+0200}, title = {Wilsonian renormalization as a quantum channel and the separability of fixed points}, url = {https://link.aps.org/doi/10.1103/PhysRevD.107.125014}, volume = 107, year = 2023 }