Global quantum discord in the Lipkin–Meshkov–Glick model at zero and finite temperatures

Abstract

We study the global quantum discord (GQD) in the Lipkin-Meshkov-Glick (LMG) model at zero and finite temperatures, in which all spins are mutually interacted and introduced in an external magnetic field (denoted by $h$). We confirm that the high coordinate number is one of the most distinguishing features of the LMG model, which directly results in the nontrivial behaviors of quantum correlations. We compare the GQD with other quantum correlations measures (such as concurrence, quantum discord, and global entanglement) and find the remarkable difference between them. For instance, we find that GQD spreads in the entire system and captures more information on quantum correlations when comparing with concurrence and quantum (pairwise) discord. We discover that GQD can characterize multipartite correlations in the both broken phase ($h0$ in the anisotropic cases for any fixed magnetic field. We further show that GQD behaves as $\mathcal{G}|_{s_n} \sim k \cdot \frac{1}{N}+c$ with $k<0$ in the isotropic cases for any Dicke state $|s_n\rangle$. Herein $k$ and $c$ are the fitting parameters. We also find that the thermal stability of the GQD at low temperatures depends on the energy gap. We further reveal that the extraordinary behaviors of the thermal-state GQD in the isotropic LMG model are explained by the contribution theory of the energy levels.