Entanglement sudden death induced by the Dzialoshinskii--Moriya interaction

In this paper, we study the entanglement dynamics of two-spinHeisenberg XYZ model with the Dzialoshinskii--Moriya (DM)interaction. The system is initially prepared in the Werner state.The effects of purity of the initial state and DM coupling parameteron the evolution of entanglement are investigated. The necessary andsufficient condition for the appearance of the entanglement suddendeath (ESD) phenomenon has been deduced. The result shows that theESD always occurs if the initial state is sufficiently impure forthe given coupling parameter or the DM interaction is sufficientlystrong for the given initial state. Moreover, the critical values ofthem are calculated.