Interplay between anisotropic exchange coupling and the swap operation in the two-qubit Heisenberg XY model

In this Letter we investigate the interplay between Zeeman splitting and the exchange-induced swap operation in Heisenberg XY model. It is shown that the anisotropic exchange coupling can rule out the swap action even if the magnetic field is homogeneous. The time-evolution of entanglement is also studied and we find that the degree of entanglement of the two spins is suppressed in the presence of inhomogeneous magnetic fields.