  A relation between geometric phases and criticality of spin chains is
established. As a result, we show how geometric phases can be exploited as a
tool to detect regions of criticality without having to undergo a quantum phase
transition. We analytically evaluate the geometric phase that correspond to the
ground and excited states of the anisotropic XY model in the presence of a
transverse magnetic field when the direction of the anisotropy is adiabatically
rotated. Ultra-cold atoms in optical lattices are presented as a possible
physical realization.
