Entanglement Entropy beyond the Free Case

TL;DR

This paper introduces a perturbative approach to calculate entanglement entropy in interacting quantum systems, demonstrating its effectiveness on a spin model and revealing critical scaling behaviors.

Contribution

It develops a new perturbative method for entanglement entropy in interacting systems and applies it to a collective spin model, providing analytical and numerical agreement.

Findings

Entanglement entropy scales logarithmically at the quantum critical point.

Scaling prefactors depend on subsystem size, system size, and anisotropy.

Finite-size corrections to entropy are analytically evaluated.

Abstract

We present a perturbative method to compute the ground state entanglement entropy for interacting systems. We apply it to a collective model of mutually interacting spins in a magnetic field. At the quantum critical point, the entanglement entropy scales logarithmically with the subsystem size, the system size, and the anisotropy parameter. We determine the corresponding scaling prefactors and evaluate the leading finite-size correction to the entropy. Our analytical predictions are in perfect agreement with numerical results.