  We study the connection between Berry phases and quantum phase transitions of
generic quantum many-body systems. Consider sequences of Berry phases
associated to sequences of loops in the parameter space whose limit is a point.
If the sequence of Berry phases does not converge to zero, then the limit point
is a quantum critical point. Quantum critical points are associated to failures
of adiabaticity. We discuss the remarkable example of the anisotropic XY spin
chain in a transverse magnetic field and detect the XX region of criticality.
