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We investigate disentanglement dynamics of two coupled qubits and qutritswhich interact uniformly to a general XY spin-chain environment with theDzyaloshinsky-Moriya (DM) interaction. We obtained exact expression of the timeevolution operator and analyzed the dynamical process of the decoherencefactors. Through explicitly calculating the concurrence and the negativity, weexamined disentanglement behaviors of two coupled central spins evolve fromdifferent initial pure states, which are found to be nontrivially differentfrom those of the uncorrelated ones, in particular, the enhanced decay of theentanglement induced by quantum criticality of the surrounding environment maybe broken by introducing self-Hamiltonian of the central spin system. Moreover,the DM interaction may have different influences on decay of the entanglementdepending on the strength of the system-environment coupling, the anisotropy ofthe environmental spin chain and the intensity of the transverse magneticfield, as well as the explicit form of the initial states of the central spinsystem.

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky-Moriya interaction