Renyi relative entropies and renormalization group flows

TL;DR

This paper explores quantum Renyi relative entropies in the context of renormalization group flows, deriving new inequalities and applying them to a Kondo model to understand thermodynamic-like behavior in quantum field theory.

Contribution

It introduces explicit expressions for Renyi relative entropies in free field theory and establishes new inequalities that govern RG flows, linking them to thermodynamic principles.

Findings

Derived explicit formulas for Renyi relative entropies in free fields

Established new inequalities for RG trajectories based on monotonicity

Applied results to a Kondo model, avoiding Anderson's orthogonality catastrophe

Abstract

Quantum Renyi relative entropies provide a one-parameter family of distances between density matrices, which generalizes the relative entropy and the fidelity. We study these measures for renormalization group flows in quantum field theory. We derive explicit expressions in free field theory based on the real time approach. Using monotonicity properties, we obtain new inequalities that need to be satisfied by consistent renormalization group trajectories in field theory. These inequalities play the role of a second law of thermodynamics, in the context of renormalization group flows. Finally, we apply these results to a tractable Kondo model, where we evaluate the Renyi relative entropies explicitly. An outcome of this is that Anderson's orthogonality catastrophe can be avoided by working on a Cauchy surface that approaches the light-cone.