Entanglement of a two-qubit system with anisotropic XYZ exchange coupling in a nonuniform time-dependent external magnetic field

The dynamics of entanglement of a two-qubit system coupled through anisotropic XYZ Heisenberg interaction is considered. We study the system in presence of a time-varying nonuniform magnetic field. Both analytical and numerical solutions for the entanglement are given. We find that the spin space of the system at any time is divided into two separate subspaces which never get mixed as the system evolves in time. Furthermore each subspace is controlled by a different independent set of parameters. At certain critical values of the exchange coupling and magnetic field parameters which specify the boundary between the two subspaces, the entanglement of the ground state shows a discontinuous behavior. The discontinuity of the entanglement continues with varying magnitude as the system evolves in time. We also realize that, although the system is explicitly time-dependent, however, it can be initially prepared in minimally or maximally entangled ground state in any one of the two subspaces which is a stationary state of the Hamiltonian. The results show that the amount of entanglement between the two qubits is sensitive to different parameters of the applied magnetic field as well as to the strength of the different exchange coupling components.