Berry phases in superconducting transitions

I generalize the concept of Berry's geometrical phase for quasicyclic Hamil tonians to the case in which the ground state evolves adiabatically to an e xcited state after one cycle, but returns to the ground state after an inte ger number of cycles. This allows to extend the charge Berry phase gamma(c) related to the macroscopic polarization, to many-body systems with fractio nal number of particles per site. Under certain conditions, gamma(c) and th e spin Berry phase gamma(s) jump in pi at the boundary of superconducting p hases. In the extended Hubbard chain with on-site attraction U and nearest- neighbor interaction V at quarter filling, the transitions detected agree v ery well with exact results in two limits solved by the Bethe ansatz, and w ith previous numerical studies. In chains with spin SU(2) symmetry, gamma(s ) jumps when a spin gap opens.