Multipartite nonlocality and global quantum discord in the antiferromagnetic Lipkin–Meshkov–Glick model

Abstract

We have investigated the multipartite nonlocality and global quantum discord (GQD) in the antiferromagnetic Lipkin–Meshkov–Glick (LMG) model. We find that nonlocality and GQD can indicate quantum phase transitions by singular behaviors. The results also show that GQD always behaves a linear growth with log10N in the LMG model, which is different from linear scaling in one-dimensional chains. And this scaling behavior is not affected by anisotropic parameter γ. Moreover, the nonlocality (denoted by S) is discovered to scale as log10S|h∼aN+b for the transverse-field LMG model (i.e., γ=0). However, scaling behaviors can be well fitted by formula S|h=a1N+b for the LMG model with γ>0. By comparing the results of GQD and nonlocality, we have observed that nonlocality decreases but GQD increases as the size of the system grows. These results indicate that γ has a significant influence on the nonlocality and GQD in the LMG model.