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 log 10 N 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 log 10 S | h ∼ a N + b for the transverse-field LMG model (i.e., γ = 0 ). However, scaling behaviors can be well fitted by formula S | h = a 1 N + 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.