Probing ππ-tangle and quantum phase transition in the one-dimensional anisotropic XY model with Dzyaloshinskii–Moriya interaction

In this paper, the effect of Dzyaloshinskii–Moriya interaction and anisotropy on the ππ-tangle and quantum phase transition (QPT) by employing the QRG method in the one-dimensional anisotropic XY model is investigated. In our model the anisotropy and DM interaction parameters can influence the phase diagrams. While the anisotropy suppresses the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. When the value of DM interaction is certain, the ππ-tangle develops into two different values which separate the system into two phases i.e. the spin-fluid phase and the Néel phase with the number of QRG iterations increased. Meanwhile, the ππ-tangle decreases slowly as the sites of the chain became larger, but the ππ-tangle tends to be a fixed value finally. Additionally, it exhibits a maximum for the next-nearest-neighbor entanglement at the critical point in our model which is different from the situation of the two-body system. To gain further insight, the nonanalytic and scaling behaviors of ππ-tangle have also been analyzed in detail and this phenomenon indicates that the behavior of the entanglement can perfectly help one to observe the quantum critical properties of the model.