Thermal entanglement versus mixture in a spin chain: Generation of maximally entangled mixed states

We study the two-body entanglement and mixture in a three-qubit XXZ spin chain in thermal equilibrium state at temperature T with an external magnetic field B. The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered. We show that the ground states in this system are fully characterized and distinguished by both entanglement and mixture. Thermal entanglement versus the mixture of all two-spin states is investigated. All pairwise states provide an upper bound on the entanglement for a fixed mixture, and some part of the boundary reaches the boundary allowed by physics. As a result, maximally entangled mixed states can be generated by controlling magnetic field and temperature. Especially, in the ground state of the whole system, the explicit forms of maximally entangled mixed states are given. The results provide a new way to generate maximally entangled mixed states and control entanglement.