Induced decoherence and entanglement by interacting quantum spin baths

Abstract

The reduced dynamics of a single qubit or two qubits coupled to an interacting quantum spin bath modeled by an $XXZ$ spin chain is investigated. By using the method of a time-dependent density matrix renormalization group $(t\text{-DMRG})$, we go beyond the uniform coupling central spin model and nonperturbatively evaluate the induced decoherence and entanglement. It is shown that both the decoherence and the 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 the qubits directly couple to the order parameter, the reduced dynamics shows an oscillatory type behavior. On the other hand, only for the paramagnetic and the antiferromagnetic phases do the initially entangled states suffer from an entanglement sudden death. By calculating the concurrence, the finite disentanglement time is mapped out for all of the phases in the phase diagram of the spin bath.