  We obtain exact dynamics of a two-qubit central spin model (CSM) consisting
of two interacting qubits homogeneously coupled to a spin bath via the
$XXZ$-type coupling, with the bath initially prepared in linear superpositions
of the symmetric Dicke states. Using the interaction picture Hamiltonian with
respect to the non-spin-flipping part of the model, we derive a sequence of
equations of motion within each magnetization sector satisfied by the
probability amplitudes of the time-evolved state. These equations of motion
admit analytical solutions for the single-qubit CSM in which one of the two
central qubits decouples from the rest of the system. Based on this, we provide
a quantitative interpretation to the observed collapse-revival phenomena in the
single-qubit Rabi oscillations when the bath is prepared in the spin coherent
state. We then study the disentanglement and coherence dynamics of two
initially entangled noninteracting qubits when the two qubits interact with
individual baths or with a common bath. For individual baths the coherent
dynamics is found to positively correlated to the single-qubit purity dynamics,
and entanglement sudden disappearance and revivals are observed in both cases.
The entanglement creation of two initially separable qubits coupled to a common
bath is also studied and collapse and revival behaviors in the entanglement
dynamics are observed. Choosing the equally weighted state and the $W$-class
states as the bath initial states, we finally study the dynamics of
entanglement between two individual bath spins and demonstrate the entanglement
sharing mechanism in such a system.
