Isotropic X-Y chain in an inhomogeneous magnetic field

J.P. de Lima, T. F. A. Alves, L.L. Gonçalves

A. C. Dolgov

D. Tian

We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.

Cenk Akyüz, Ekrem Aydmer

We have numerically calculated the thermal entanglement of a two-qubit system at low temperatures in a isotropic Ising chain under an inhomogeneous magnetic field. It is shown that in the homogeneous magnetic field, the two-qubit system has entangled states. It is concluded that the presence of the inhomogeneity in the magnetic field plays an effective role on the entangled states. Finally, it is suggested that the inhomogeneity in the magnetic field can be used to create two separated entangled formations in a two-qubit system.

Tôru Sakai, Minoru Takahashi