  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.
