Entanglement Entropy of Yukawa-Coupled Fields Across a Rindler Horizon

TL;DR

This paper calculates the entanglement entropy across a Rindler horizon in a Yukawa-coupled scalar field theory, revealing how interactions modify the area law and depend on the screening mass and UV cutoff.

Contribution

It introduces a microscopic, nonlocal kernel method to compute entanglement entropy in interacting quantum fields without relying on replica or geometric techniques.

Findings

Entanglement entropy obeys an area law with interaction-induced corrections.

Corrections depend on the Yukawa screening mass and UV cutoff logarithmically.

The entanglement spectrum is independent of the Rindler observer's acceleration.

Abstract

We compute the entanglement entropy across a Rindler horizon in scalar field theory with Yukawa interaction. Starting from a microscopic scalar-mediator theory in flat spacetime, we integrate out the massive mediator to obtain a quadratic but nonlocal effective kernel that determines the ground-state wavefunctional. The reduced density matrix for a single Rindler wedge is constructed explicitly by tracing over the complementary wedge, allowing the entanglement entropy to be evaluated directly from the kernel without replica or geometric methods. Exploiting translational invariance parallel to the horizon, the problem decomposes into independent transverse momentum sectors that reduce effectively to one-dimensional nonlocal systems and can be diagonalized analytically in the weak-coupling regime. The interaction-induced entropy obeys an area law, with leading corrections controlled by the Yukawa screening mass and logarithmically sensitive to the transverse ultraviolet cutoff, reflecting the localization of correlations near the horizon. Although the modular Hamiltonian depends on the Rindler acceleration, the entanglement spectrum and entropy are independent of this choice, demonstrating the observer-independent nature of vacuum entanglement. Our framework provides a direct and microscopically transparent approach to computing interaction-induced corrections to horizon entanglement using nonlocal effective kernels.