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Taking the decoherence effect due to population relaxation into account, weinvestigate the entanglement properties for two qubits in the Heisenberg XYinteraction and subject to an external magnetic field. It is found that thephenomenon of entanglement sudden death (ESD) as well as sudden birth(ESB)appear during the evolution process for particular initial states. Theinfluence of the external magnetic field and the spin environment on ESD andESB are addressed in detail. It is shown that the concurrence, a measure ofentanglement, can be controlled by tuning the parameters of the spin chain,such as the anisotropic parameter, external magnetic field, and the couplingstrength with their environment. In particular, we find that a criticalanisotropy constant exists, above which ESB vanishes while ESD appears. It isalso notable that stable entanglement, which is independent of differentinitial states of the qubits, occurs even in the presence of decoherence.

Sudden death, birth and stable entanglement in a two-qubit Heisenberg XY spin chain