Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model

TL;DR

This paper demonstrates that in the Lipkin-Meshkov-Glick model, different entanglement measures exhibit equivalent critical scaling laws, contrasting with behavior in one-dimensional systems, and provides analytical proofs for these relations.

Contribution

It establishes a novel analytical connection between various entanglement measures in the Lipkin-Meshkov-Glick model at criticality.

Findings

Single-copy entanglement scales like entanglement entropy near criticality

Global geometric entanglement exhibits similar critical behavior

Contrasts with one-dimensional spin systems where measures differ

Abstract

We establish a relation between several entanglement properties in the Lipkin-Meshkov-Glick model, which is a system of mutually interacting spins embedded in a magnetic field. We provide analytical proofs that the single-copy entanglement and the global geometric entanglement of the ground state close to and at criticality behave as the entanglement entropy. These results are in deep contrast to what is found in one- dimensional spin systems where these three entanglement measures behave differently.