ar X iv : 0 90 3 . 06 30 v 2 [ qu an t - ph ] 1 3 M ay 2 00 9 Dzyaloshinskii - Moriya Interaction and Anisotropy effects on the Entanglement of Heisenberg Model

In this paper the the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the Entangle-ment of Heisenberg model has been studied. While the anisotropy suppress the entanglement due to favoring of the alignment of spins, the DM interaction restore the spoiled entanglement via the introduction of the quantum fluctuations. Thermodynamic limit of the model and emerging of non-analytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The effect of gapped and gapless phases of the model on the features of the entanglement has also been discussed.