Wilsonian Effective Action and Entanglement Entropy

TL;DR

This paper extends the understanding of entanglement entropy in interacting quantum field theories by unifying contributions from propagators and vertices, and explores their relation to Wilsonian renormalization group flow.

Contribution

It introduces a unified matrix form of entanglement entropy and proposes that IR EE is given by vertex contributions in the Wilsonian effective action.

Findings

Unified matrix form of EE including propagator and vertex contributions

Non-Gaussian vertex contributions interpreted as renormalized composite operator correlations

Conjecture that IR EE sums all vertex contributions in the Wilsonian effective action

Abstract

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In arXiv:2103.05303, we have proposed the notion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. As shown in the next paper arXiv:2105.02598, the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.