Effect of Dzyaloshinskii-Moriya Interaction on the Entanglement and Quantum Phase Transition in Two-Dimensional XXZ Model

We investigate the effect of Dzyaloshinskii-Moriya interaction and the anisotropy on the entanglement of the two-dimensional Heisenberg XXZ model. Concurrence and quantum Fisher information are computed to witness the entanglement. It is observed that the anisotropy suppresses the concurrence and this suppression can be compensated by the Dzyaloshinskii-Moriya interaction.We solved the model by using quantum renormalization group method and computed the unstable fixed points of the model and obtained the phase diagram of the model. In phase diagram, the critical line separates the two phases, the spinfluid phase and the N´eel phase. Interestingly, a variation in the quantum phase transition of the model is observed while tuning the Dzyaloshinskii-Moriya interaction. At phase transition point, the non analyticity using first derivative and the scaling behavior is studied for both, the concurrence and the quantum Fisher information. Moreover, the scaling exponent successfully describes the correlation length of the model at the critical point.