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

We investigate disentanglement dynamics of two coupled qubits and qutrits which interact uniformly to a general XY spin-chain environment with the Dzyaloshinsky-Moriya (DM) interaction. We obtained exact expression of the time evolution operator and analyzed the dynamical process of the decoherence factors. Through explicitly calculating the concurrence and the negativity, we examined disentanglement behaviors of two coupled central spins evolve from different initial pure states, which are found to be nontrivially different from those of the uncorrelated ones, in particular, the enhanced decay of the entanglement induced by quantum criticality of the surrounding environment may be broken by introducing self-Hamiltonian of the central spin system. Moreover, the DM interaction may have different influences on decay of the entanglement depending on the strength of the system-environment coupling, the anisotropy of the environmental spin chain and the intensity of the transverse magnetic field, as well as the explicit form of the initial states of the central spin system.