Electric polarization in correlated insulators

We derive a formula for the electric polarization of interacting insulators, expressed in terms of the full Green's and vertex functions. We exemplify this method in the half-filled ionic Hubbard model treated within dynamical mean field theory (DMFT). The electric polarization of a correlated band insulator is determined by the interplay of ionicity and covalency, and both quantities are renormalized by the electron-electron interactions. We introduce quasiparticle approximations to the exact equation for the polarization, and compare the results of these approximations with those of the exact DMFT formulation and of static mean field theories such as the LDA+U. The latter overestimates the electronic contribution to the electric polarization when the quasiparticle weight of the active bands is very small.