Geometric Phase and Fidelity of The One-Dimensional Extended Quantum Compass Model in a Transverse Field

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.