The thermal entanglement in a two-qubit Heisenberg $XXZ$ spin chain is investigated under an inhomogeneous magnetic field $b$. We show that the ground-state entanglement is independent of the interaction of $z$-component $J_z$. The thermal entanglement at the fixed temperature can be enhanced when $J_z$ increases. We strictly show that for any temperature $T$ and $J_z$, the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field $b_c$ is independent of $J_z$. The critical magnetic field $B_c$ increases with the increasing $\mid b\mid$ but the maximum entanglement value that the system can arrive at becomes smaller.

• Received 15 March 2005

DOI:https://doi.org/10.1103/PhysRevA.72.034302