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

TL;DR

This paper demonstrates that Wilsonian RG acts as a quantum channel, implying fixed point vacua are unentangled across momentum scales, revealing new insights into their structure and symmetries.

Contribution

It introduces a novel perspective by interpreting Wilsonian RG as a quantum channel, linking scale invariance to entanglement properties of fixed point vacua.

Findings

Fixed points have no entanglement between momentum scales.

Scale symmetry constrains the ground state and momentum space operator expectations.

Wilsonian RG can be viewed as a quantum information process.

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.