Pairwise entanglement of two impurities in the XY model

We propose a general method to solve the anisotropic XY model with two impurities on the period boundary condition. On the basis of exact solution, we discuss the impurity excitations in detail. The results indicate that the critical behaviors of the system near the critical point are closely related to the particle excitations. We investigate the quantum phase transition and the pairwise entanglement of the nearest-neighbors impurities, and find that the singular behaviors of pairwise entanglement near the critical point are naturally derived from the competition between impurity excitation and normal fermion excitation. When the two impurities are separated at certain distance, the pairwise entanglements oscillate with the variation of the distance, and the oscillations diminish with the increase of the distance. The couple interaction and anisotropy of impurity both can control the pairwise entanglement, however, this effects strongly depend on the order state of the system. - Highlights: • By introducing a proper displacement quantity of impurity, this method can be applied in complex spin model. • The pairwise entanglement of impurities can be controlled by the coupling and anisotropy of impurity. • The singular behaviors of the pairwise entanglement are closely related to the particle excitation.