Universality of the negativity in the Lipkin-Meshkov-Glick model

TL;DR

This paper investigates the logarithmic negativity in the Lipkin-Meshkov-Glick model, revealing its universal behavior at criticality for tripartitions and its divergence for bipartitions, indicating a deep link with entanglement entropy.

Contribution

It provides the first analytic study of entanglement negativity between noncomplementary blocks in the LMG model, uncovering its universal properties at critical points.

Findings

Negativity is finite and universal at criticality for tripartitions.

Negativity diverges for bipartitions, behaving like entanglement entropy.

A potential universal relation between negativity and entanglement entropy is suggested.

Abstract

The entanglement between noncomplementary blocks of a many-body system, where a part of the system forms an ignored environment, is a largely untouched problem without analytic results. We rectify this gap by studying the logarithmic negativity between two macroscopic sets of spins in an arbitrary tripartition of a collection of mutually interacting spins described by the Lipkin-Meshkov-Glick Hamiltonian. This entanglement measure is found to be finite and universal at the critical point for any tripartition whereas it diverges for a bipartition. In this limiting case, we show that it behaves as the entanglement entropy, suggesting a deep relation between the scaling exponents of these two independently defined quantities which may be valid for other systems.