Electric polarization in correlated insulators

TL;DR

This paper develops a formula for electric polarization in interacting insulators using Green's functions, demonstrating its application in the ionic Hubbard model within DMFT, and compares different approximation methods.

Contribution

It introduces a Green's function-based formula for polarization in correlated insulators and compares quasiparticle and mean-field approximations.

Findings

Quasiparticle approximation closely matches exact DMFT results.

Static mean field theories overestimate polarization in strongly correlated regimes.

Electron-electron interactions significantly renormalize ionicity and covalency.

Abstract

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 approximation to the exact equation for the polarization, and compare the results of this approximation 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.