QUANTUM PHASE-TRANSITIONS INVOLVING A CHANGE IN POLARIZATION

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.