  It is known that an interacting bipartite system evolves as an entangled
state in general, even if it is initially in a separable state. Due to the
entanglement of the state, the geometric phase of the system is not equal to
the sum of the geometric phases of its two subsystems. However, there may exist
a set of states in which the nonlocal interaction does not affect the
separability of the states, and the geometric phase of the bipartite system is
then always equal to the sum of the geometric phases of its subsystems. In this
paper, we illustrate this point by investigating a well known physical model.
We give a necessary and sufficient condition in which a separable state remains
separable so that the geometric phase of the system is always equal to the sum
of the geometric phases of its subsystems.
