Quantum correlations in the collective spin systems

TL;DR

This paper analytically and numerically investigates quantum and classical correlations in collective spin systems, revealing universal behaviors of quantum discord near critical points and comparing it with entanglement measures.

Contribution

It provides the first large-size scaling analysis of quantum discord in critical spin models and identifies universal divergence behaviors at phase transitions.

Findings

Quantum discord exhibits logarithmic divergence in its first derivative at critical points.

Quantum discord is small in one phase and robust in the other, contrasting with concurrence behavior.

Large-size scaling of quantum discord reveals universal critical behavior in collective spin systems.

Abstract

Quantum and classical pairwise correlations in two typical collective spin systems (i.e., the Dicke model and the Lipkin-Meshkov-Glick model) are discussed. These correlations in the thermodynamical limit are obtained analytically and in a finite-size system are calculated numerically. Large-size scaling behavior for the quantum discord itself is observed, which has never been reported in another critical system. A logarithmic diverging behavior for the first derivative of the quantum discord is also found in both models, which might be universal in the second-order quantum phase transition. It is suggested that the pronounced maximum or minimum of first derivative of quantum discord signifies the critical point. Comparisons between the quantum discord and the scaled concurrence are performed. It is shown that the quantum discord is very small in one phase and robust in the other phase, while the scaled concurrence shows maximum at the critical point and decays rapidly when away from the the critical point.