  We show that geometric phase of the ground state in the XY model obeys
scaling behavior in the vicinity of a quantum phase transition. In particular
we find that geometric phase is non-analytical and its derivative with respect
to the field strength diverges at the critical magnetic field. Furthermore,
universality in the critical properties of the geometric phase in a family of
models is verified. In addition, since quantum phase transition occurs at a
level crossing or avoided level crossing and these level structures can be
captured by Berry curvature, the established relation between geometric phase
and quantum phase transitions is not a specific property of the XY model, but a
very general result of many-body systems.
