Quantum correlations and quantum phase transition in the Ising model with Dzyaloshinskii-Moriya interaction

In this paper, we investigate quantum correlations (QCs) and quantum phase transition (QPT) in the Ising model with Dzyaloshinskii-Moriya (DM) interaction by employing the quantum renormalization group method. The results show that some quantum correlation measures can effectively exhibit the quantum critical points associated with quantum phase transition after several iterations of the renormalization. The results also show the geometric quantum discord (GQD) is an upper bound of the square quantum discord (QD) (or negativity) in this spin system all along. Moreover, the nonanalytic appearance and scaling behaviors of the model are analyzed in detail. As a byproduct, we obtain that quantum discord is equal to negativity when the parameter of the DM interaction is small while quantum discord is larger than negativity when the spin-orbit has a strong coupling effect.