Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
High Energy Physics - Theory
2023-06-28 v2 Statistical Mechanics
Quantum Physics
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.
Cite
@article{arxiv.2211.10238,
title = {Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points},
author = {Matheus H. Martins Costa and Jeroen van den Brink and Flavio S. Nogueira and Gastão I. Krein},
journal= {arXiv preprint arXiv:2211.10238},
year = {2023}
}
Comments
v2: main sections expanded for clarity, discussion added on the scaling of the time variable and the associated dynamical critical exponent, references added and other minor changes, 7 pages