Entanglement in a second order quantum phase transition

TL;DR

This paper investigates how entanglement and spin squeezing behave in a system of interacting spins undergoing a second order quantum phase transition, revealing singularities and changes in quantum correlations at criticality.

Contribution

It provides a detailed analysis of entanglement and spin squeezing in a second order quantum phase transition, highlighting differences from the one-dimensional case and identifying critical points.

Findings

A cusp-like singularity appears at the critical point in the thermodynamic limit.

There exists a threshold value where the ground state loses spin squeezing despite non-zero concurrence.

Entanglement properties exhibit distinct behavior compared to one-dimensional systems.

Abstract

We consider a system of mutually interacting spin 1/2 embedded in a transverse magnetic field which undergo a second order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusp-like singularity appears at the critical point $\lambda_c$, in the thermodynamic limit. We also show that there exists a value $\lambda_0 \geq \lambda_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.