The geometric Berry's phase of the many-body wave function can be used
to characterize changes in the electric polarization at quantum phase
transitions that take place as one parameter of the Hamiltonian is ad
iabatically changed. Transitions which involve a discontinuous change
in macroscopic polarization are of topological nature, and occur whene
ver the system exhibits planes of inversion symmetry. We have applied
these ideas to a variety of strongly correlated lattice fermion models
in one and two dimensions; in particular, the three-band Hubbard mode
l in CuO2 planes in the parent compounds of high-temperature supercond
uctors. For spin-1/2 fermions, we find that the transition between a q
uantum paramagnet and an antiferromagnet is one of those topological t
ransitions, thus establishing an interesting relation between electric
polarization and antiferromagnetism. Interesting consequences emerge
when one considers insulators separated by domain walls: A net accumul
ation of charge at the interface results, which is easily calculated f
rom the Berry's phase change at the domain wall. We discuss the connec
tion to the recently proposed (and experimentally observed) ''microsco
pic stripes'' in nickelate and insulating cuprate materials.