Entanglement of a degenerate system in adiabatic process

Entanglement evolution of a degenerate system is studied. It is found that an entangled state becomes unentangled under an adiabatic variation of the system, and vice versa. The amount of entanglement varies with different adiabatic paths. It is concluded that the entanglement of complete set of eigenstates of a system at thermal equilibrium is independent on perturbations, but the entanglement of partial eigenstates may change with adiabatic perturbations. This can help us to control entanglement properties and is very useful in the quantum computations.