  We study the geometric phase of the ground state in the extended quantum
compass model in presence of a transverse field. The exact solution is obtained
by using the Jordan-Wigner transformation which maps the Hamiltonian on a
fermionic system and applying the Fourier transformation to realize the
diagonalization and an analytical expression for the ground state and geometric
phase in the momentum space. Furthermore, the scaling behavior of the extremum
of geometric phase and its universality are investigated due to the divergence
of geometric phase at the critical point.
