  Realizable spin models are investigated in a two superconducting flux qubit
system. It is shown that a specific adjustment of system parameters in the two
flux qubit system makes it possible to realize an artificial two-spin system
that cannot be found naturally. For the artificial two-spin systems, time
evolution of a prepared quantum state is discussed to quantify quantum
entanglement dynamics. The concurrence and fidelity as a function of time are
shown to reveal a characteristic entanglement dynamics of the artificial spin
systems. It is found that the unentangled input state can evolute to be a
maximally entangled output state periodically due to the exchange interactions
induced by two-qubit flipping tunneling processes while single-qubit flipping
tunneling processes plays a role of magnetic fields for the artificial spins.
