Geometric R\'enyi mutual information induced by localized particle excitations in quantum field theory

TL;DR

This paper investigates how localized particle excitations in a quantum field affect spatial correlations, revealing that such excitations generate finite, boundary-maximized correlations that decay with distance, advancing understanding of quantum correlations in field theory.

Contribution

It introduces a method to quantify the Renyi mutual information for localized excitations in quantum fields, highlighting excitation-induced correlations and their spatial behavior.

Findings

Excitations produce finite, positive correlations.

Correlations are maximized at the boundary.

Correlation strength decreases with distance from the boundary.

Abstract

Quantum field theory exhibits rich spatial correlation structures even in the vacuum, where entanglement entropy between regions scales with the area of their shared boundary. While this vacuum structure has been extensively studied, far less is understood about how localized particle excitations influence correlations between field values in different spatial regions. In this work, we use the Schr\"odinger representation to study the R\'enyi mutual information between complementary spatial regions for a localized single-particle excitation of a free massless scalar field in $(d+1)$ dimensions. We find that the mutual information in this excited state includes both a vacuum term and an excitation-induced contribution. To obtain quantitative results, we specialize to $1+1$ dimensions and evaluate the R\'enyi-2 mutual information between the negative and positive halves of the real line. We find that the excitation generates finite, positive correlations that are maximized when the wave packet sits at the boundary and decrease with its distance from it, at a rate determined by the wave packet's width. Our findings offer a step towards understanding quantum correlations in multiparticle systems from a field-theoretical point of view.