Geometric Rényi mutual information induced by localized particle excitations in quantum field theory

TL;DR

This work analyzes how a localized single-particle excitation modifies geometric correlations in a free massless scalar quantum field by working in the Schrödinger representation to construct localized states and using replica techniques to compute Rényi mutual information between complementary regions. The authors derive that, in general, the mutual information splits into a vacuum term and a finite excitation-induced contribution, with explicit results in 1+1D for the Rényi-2 entropy of half-line regions. They find finite, positive excitation-induced corrections that peak when the wave packet sits at the boundary and decay with distance and packet width, and demonstrate a left–right splitting over time that yields a nonzero asymptotic correction $\ln(32/25)$ to the mutual information. Overall, the paper provides a tractable field-theoretic framework to study spatial correlations in multiparticle states and points toward extensions to two-particle states and dynamical entanglement in quantum field theory, anchored by explicit determinant and Poisson-kernel constructions.

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 Schrödinger representation to study the Rényi 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 Rényi-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.

Figures (5)

• Figure 1: Evolution of the squared absolute value of the wave packet $f(t,x)$ given by \ref{['Lorentzian wave packet for tneq0']}, with $\alpha=1$ and $\langle x \rangle=0$.
• Figure 2: Rényi-2 entropy corrections for the regions $\Omega$ and $\overline{\Omega}$ at $t=0$.
• Figure 3: Time evolution of the Rényi-2 entropy correction for the region $\Omega$ (with $\alpha=0.1$), for different values of $\langle x \rangle$.
• Figure 4: The additional Rényi-2 mutual information due to the particle, at $t=0$.
• Figure 5: The additional mutual information due to the particle as a function of time, with $\alpha=0.1$.