  The notion of geometric phase has been recently introduced to analyze the
quantum phase transitions of many-body systems from the geometrical
perspective. In this work, we study the geometric phase of the ground state for
an inhomogeneous period-two anisotropic XY model in a transverse field. This
model encompasses a group of familiar spin models as its special cases and
shows a richer critical behavior. The exact solution is obtained by mapping on
a fermionic system through the Jordan-Wigner transformation and constructing
the relevant canonical transformation to realize the diagonalization of the
Hamiltonian coupled in the $k$-space. The results show that there may exist
more than one quantum phase transition point at some parameter regions and
these transition points correspond to the divergence or extremum properties of
the Berry curvature.
