A Lindbladian for exact renormalization of density operators in QFT

TL;DR

This paper derives a Lindblad master equation for the exact renormalization group flow of density operators in quantum field theory, revealing the dissipative structure and its implications for state distinguishability.

Contribution

It introduces a Lindbladian framework for ERG flow of density matrices in QFT, connecting renormalization with open quantum system dynamics.

Findings

ERG flow of density matrices is governed by a Lindblad equation

Dissipative terms generate correct coupling flow in QFT

Finite ERG flow corresponds to a quantum channel with monotonic distinguishability

Abstract

In arXiv:1609.03493, the authors extended the exact renormalization group (ERG) to arbitrary wave-functionals in quantum field theory (QFT). Applying this formalism, we show that the ERG flow of density matrices is given by a Lindblad master equation. The Lindbladian consists of a "Hamiltonian" term which is the sum of a scaling and a coarse-graining (disentangling) operator, and a dissipative term with absorption and emission rates for each momentum mode. We consider as examples the flow of Gaussian states and the perturbative ground state of $\lambda \phi^4$ theory, and highlight the role of the dissipative terms in generating the correct flow of couplings. Integrating the Lindblad master equation, we find that a finite ERG flow of density matrices is described by a quantum channel. It follows from the data processing inequality that any distinguishability measure of states is an ERG monotone.