Momentum Space Entanglement from the Wilsonian Effective Action

TL;DR

This paper introduces a new method to compute momentum space entanglement entropy in quantum field theories using the Wilsonian effective action, providing a perturbative approach that simplifies calculations and can be extended to nonperturbative regimes.

Contribution

A novel technique connecting Wilsonian effective actions with momentum space entanglement entropy calculations, avoiding matrix diagonalizations and applicable to higher-order analyses.

Findings

Validated the method with scalar theories at lowest order

Compared results with existing literature and Feynman diagram interpretations

Demonstrated the method's potential for nonperturbative extensions

Abstract

The entanglement between momentum modes of a quantum field theory at different scales is not as well studied as its counterpart in real space, despite the natural connection with the Wilsonian idea of integrating out the high-momentum degrees of freedom. Here, we push such connection further by developing a novel method to calculate the R\'enyi and entanglement entropies between slow and fast modes, which is based on the Wilsonian effective action at a given scale. This procedure is applied to the perturbative regime of some scalar theories, comparing the lowest-order results with those from the literature and interpreting them in terms of Feynman diagrams. This method is easily generalized to higher-order or nonperturbative calculations. It has the advantage of avoiding matrix diagonalizations of other techniques.