Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction

This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii--Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states \cos \theta \left\vert 00\right\rangle +\sin \theta \left\vert 11\right\rangle and \cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle at zero temperature. The influences of Dzyaloshinskii--Moriya interaction D, anisotropic parameter \varDelta and environment coupling strength \gamma on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii--Moriya interaction D acts on the time evolution of entanglement only when the initial state is \cos \phi \left\vert 01\right\rangle +\sin \phi \left\vert 10\right\rangle . Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii--Moriya interaction D, depends on the anisotropic parameter \varDelta and the environment coupling strength \gamma.