Entanglement Entropy of Yukawa-Coupled Fields Across a Rindler Horizon

TL;DR

This work analyzes how a Yukawa-type interaction modifies entanglement entropy across a Rindler horizon in a four-dimensional scalar theory. By integrating out the massive mediator, the authors obtain a quadratic but nonlocal kernel that completely specifies the ground-state wavefunctional; they then construct and diagonalize the reduced density matrix sector-by-sector in transverse momentum, revealing an area-law entropy with leading corrections set by the mediator mass and a transverse UV cutoff. They show the entanglement spectrum is observer-independent despite an acceleration-dependent modular Hamiltonian, and provide a spacetime interpretation in terms of virtual mediator exchange and conical defects in Euclidean space. The framework offers a microscopically transparent alternative to replica methods for interaction-induced horizon entanglement and is extensible to other screened interactions and horizons in curved spacetimes.

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.