Semiclassical entanglement entropy for spin-field interaction

TL;DR

This paper develops a semiclassical method to accurately describe entanglement entropy in a spin-bosonic field system using classical and complex trajectories, surpassing traditional Ehrenfest time limitations.

Contribution

It introduces a novel semiclassical framework that incorporates complex trajectories to improve entanglement entropy predictions in spin-field interactions.

Findings

Semiclassical expression for entanglement entropy derived

Complex trajectories significantly enhance accuracy

Method captures entanglement dynamics beyond Ehrenfest time

Abstract

We study a general bipartite quantum system consisting of a spin interacting with a bosonic field, with the initial state prepared as the product of a spin coherent state and a canonical coherent state. Our goal is to develop a semiclassical framework to describe the entanglement dynamics between these two subsystems. Using appropriate approximations, we derive a semiclassical expression for the entanglement entropy that depends exclusively on the trajectories of the underlying classical description. By analytically extending the classical phase space into the complex domain, we identify additional complex trajectories that significantly improve the accuracy of the semiclassical description. The inclusion of these complex trajectories allows us to capture the entanglement dynamics with remarkable precision, even well beyond the Ehrenfest time. The approach is illustrated with a representative example, where the role of real and complex trajectories in reproducing the quantum entanglement entropy is explicitly demonstrated.