  The reduced dynamics of a single or two qubits coupled to an interacting
quantum spin bath modeled by a XXZ spin chain is investigated. By using the
method of time-dependent density matrix renormalization group (t-DMRG), we go
beyond the uniform coupling central spin model and evaluate nonperturbatively
the induced decoherence and entanglement. It is shown that both decoherence and
entanglement strongly depend on the phase of the underlying spin bath. We show
that in general, spin baths can induce entanglement for an initially
disentangled pair of qubits. Furthermore, when the spin bath is in the
ferromagnetic phase, because qubits directly couple to the order parameter, the
reduced dynamics shows oscillatory type behavior. On the other hand, only for
paramagnetic and antiferromagnetic phases, initially entangled states suffer
from the entanglement sudden death. By calculating concurrence, the finite
disentanglement time is mapped out for all phases in the phase diagram of the
spin bath.
