Renormalization of multipartite entanglement near the critical point of two-dimensional XXZ model with Dzyaloshinskii–Moriya interaction

We investigate the multipartite entanglement and the trace distance for the two-dimensional anisotropic spin-12 XXZ lattice with Dzyaloshinskii–Moriya interaction. It is found that for a many-body quantum system the multipartite entanglement is more advantageous than the bipartite entanglement due to the monogamy property. Both the quantifiers, the multipartite entanglement and the trace distance, decreases with an increase in the anisotropy and the Dzyaloshinskii–Moriya interaction tends to restore the spoiled entanglement. The quantum reormalization group method is used to compute the stable and the unstable fixed points. We observe that the quantum phase transition point is independent of the chosen quantifier as the thermodynamic limit is reached. After sufficient iterations of the quantum renormalization group, we observe two different saturated values of both the quantifiers that represent two separate phases, the spin-fluid phase and the Néel phase. The first derivative and the scaling behavior of the renormalized entanglement quantifiers are calculated. At quantum phase transition point, the non-analytic behavior of the first derivative of the two quantifiers as a function of lattice size is examined and it is found that the universal finite-size scaling law is obeyed. Furthermore, we observe that at the critical point the scaling exponent for the multipartite entanglement and the trace distance can describe the correlation length of the model.