Entanglement entropy in long-range harmonic oscillators

TL;DR

This paper investigates the entanglement entropy in long-range harmonic oscillators, revealing logarithmic growth with subsystem size and deviations from conformal behavior in R'enyi entropy, using both theoretical and numerical methods.

Contribution

It provides a comprehensive analysis of entanglement entropy in LRHO, highlighting differences from short-range systems and conformal field theory predictions.

Findings

Entanglement entropy grows logarithmically with subsystem size.

R'enyi entropy shows deviations from conformal predictions.

Logarithmic dependence on correlation length in the massive case.

Abstract

We study the Von Neumann and R\'enyi entanglement entropy of long-range harmonic oscillators (LRHO) by both theoretical and numerical means. We show that the entanglement entropy in massless harmonic oscillators increases logarithmically with the sub-system size as $S=\frac{c_{eff}}{3}\log l$. Although the entanglement entropy of LRHO's shares some similarities with the entanglement entropy at conformal critical points we show that the R\'enyi entanglement entropy presents some deviations from the expected conformal behavior. In the massive case we demonstrate that the behavior of the entanglement entropy with respect to the correlation length is also logarithmic as the short range case.