  The dynamics of two coupled spins-1/2 interacting with a spin-bath via the
quantum Heisenberg XY coupling is studied. The pair of central spins served as
a quantum open subsystem are initially prepared in two types of states: the
product states and the Bell states. The bath, which consists of $N$ (in the
thermodynamic limit $N\to\infty$) mutually coupled spins-1/2, is in a thermal
state at the beginning. By the Holstein-Primakoff transformation, the model can
be treated effectively as two spin qubits embedded in a single mode cavity. The
time-evolution of the purity, z-component summation and the concurrence of the
central spins can be determined by a Laguerre polynomial scheme. It is found
that (i) at a low temperature, the uncoupled subsystem in a product state can
be entangled due to the interaction with bath, which is tested by the
Peres-Horodecki separability; however, at a high temperature, the bath produces
a stronger destroy effect on the purity and entanglement of the subsystem; (ii)
when the coupling strength between the two central spins is large, they are
protected strongly against the bath; (iii) when the interaction between the
subsystem and the bath is strong, the collapse of the two spin qubits from
their initial entangled state is fast.
