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 adiabatically changed. Transitions which involve a discontinuous change in macroscopic polarization are of topological nature, and occur whenever 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 model in ${\mathrm{CuO}}_2$ planes in the parent compounds of high-temperature superconductors. For spin-1/2 fermions, we find that the transition between a quantum paramagnet and an antiferromagnet is one of those topological transitions, thus establishing an interesting relation between electric polarization and antiferromagnetism. Interesting consequences emerge when one considers insulators separated by domain walls: A net accumulation of charge at the interface results, which is easily calculated from the Berry’s phase change at the domain wall. We discuss the connection to the recently proposed (and experimentally observed) ‘‘microscopic stripes’’ in nickelate and insulating cuprate materials. © 1996 The American Physical Society.