Entanglement and multipartite quantum correlations in two-dimensional XY model with Dzyaloshinskii–Moriya interaction

The behavior of the bipartite entanglement and multipartite quantum correlations for two dimensional square lattice of Heisenberg XY model with Dzyaloshinskii–Moriya (DM) interaction is studied in the framework of the quantum renormalization group (QRG) method. The analytical results are produced for the renormalized control parameters and a phase diagram is obtained for the model which shows the stable and unstable fix points corresponding to different phases. Concurrence and global quantum discord (GQD) are the quantifiers for the study of entanglement and quantum correlations respectively which are influenced in a different manner by the control parameters anisotropy γ and the DM interaction D. However, the behavior of the quantifiers at the critical point captures the quantum phase transition (QPT) described by the divergence of their first derivative with respect to anisotropy. It is found that the DM interactions among the spins try to recover the entanglement which is more prominent for the multipartite case. GQD is a more suitable candidate as it can describe the multipartite quantum correlations present among many spins (>2) in higher dimensions. Unlike the monogamy in entanglement the quantum correlations increase with the increasing number of the interacting spins.