Effect of spin-orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field

Abstract

The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg $XYZ$ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter $D$ and, when $D$ crosses its critical value ${D}_{c}$, the entanglement undergoes a revival. Indeed, when $D$ crosses its critical value $({D}_{c})$, the ground state entanglement tends to its maximum value $(C=1)$. Also, at finite temperatures there are revival regions in the $D\text{\ensuremath{-}}T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of $D$ and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by $D$ is not the same for ferromagnetic $({J}_{z}<0)$ and antiferromagnatic $({J}_{z}>0)$ chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of ${J}_{z}<0$. We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of ${J}_{z}<0$, this minimal entanglement can be achieved by introducing spin-orbit interaction.