Spontaneous polarization as a Berry phase of the Hartree-Fock wave function: The case of ${\mathrm{KNbO}}_3$

We have investigated the ferroelectric polarization of the perovskite oxide ${\mathrm{KNbO}}_3$ within the self-consistent Hartree-Fock (HF) method, where the crystalline orbitals are expanded over a set of localized functions. According to the modern theory, macroscopic polarization is a geometric quantum phase: here we show that—within the HF framework—polarization can be cast as a Berry phase of Slater determinants. We calculate this observable for ${\mathrm{KNbO}}_3$ in its tetragonal phase. Besides polarization, we investigate several other properties of the electronic ground state, including the broken-symmetry instability of the tetragonal structure. We therefore assess the reliability and the predictive power of the HF approach when dealing with this material, which is a paradigmatic case of intermediate ionic/covalent crystal.