  Geometric phases play a central role in a variety of quantum phenomena,
especially in condensed matter physics. Recently, it was shown that this
fundamental concept exhibits a connection to quantum phase transitions where
the system undergoes a qualitative change in the ground state when a control
parameter in its Hamiltonian is varied. Here we report the first experimental
study using the geometric phase as a topological test of quantum transitions of
the ground state in a Heisenberg XY spin model. Using NMR interferometry, we
measure the geometric phase for different adiabatic circuits that do not pass
through points of degeneracy.
