Singularity of classical and quantum correlations at critical points of the Lipkin-Meshkov-Glick model in bipartition and tripartition of spins

TL;DR

This paper investigates how classical and quantum correlations behave at critical points in the Lipkin-Meshkov-Glick model, revealing that classical correlations diverge while quantum correlations remain finite in tripartition, highlighting their different robustness.

Contribution

It provides a comparative analysis of classical and quantum correlations at critical points in bipartition and tripartition of the LMG model, showing their different singular behaviors.

Findings

Classical correlations diverge at the critical point in both bipartition and tripartition.

Quantum correlations diverge only in bipartition, remaining finite in tripartition.

Classical correlation is more robust than quantum correlation at critical points.

Abstract

We study the classical correlation (CC) and quantum discord (QD) between two spin subgroups of the Lipkin-Meshkov-Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartition, we find that the classical correlations and all the quantum correlations including the QD, the entanglement of formation (EoF) and the logarithmic negativity (LN) are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartition, however, the classical correlation is still divergent but all the quantum correlation measures remain finite at the critical point. The present result shows that the classical correlation is very robust but the quantum correlation is much frangible to the environment disturbance. The present result may also lead to the conjecture that the classical correlation is responsible for the singularity behavior of physics quantities at critical points of a many-body quantum system.