Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated. By the concept of concurrence, we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on Jz and b. The entanglement can be increased by increasing the temperature in some cases. We also find that the x-component parameter Dx has a higher critical temperature and more entanglement for a certain condition than the z-component parameter Dz.
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