Derivation of static low-energy effective models by an ab initio downfolding method without double counting of Coulomb correlations: Application to SrVO${}_3$, FeSe, and FeTe

Derivation of low-energy effective models by a partial trace summation of the electronic degrees of freedom far away from the Fermi level, called downfolding, is reexamined. We propose an improved formalism free from the double counting of electron correlation in the low-energy degrees of freedom. In this approach, the exchange-correlation energy in the local-density approximation (LDA) is replaced with the $GW$ self-energy; herewith its low-energy part associated with the double counting is subtracted. Moreover, in our formalism, the frequency dependence of the effective parameter is renormalized into the static one. We apply the formalism to SrVO${}_3$ as well as to two iron-based superconductors, FeSe and FeTe. The resultant bandwidths of the effective models are nearly the same as those of the previous downfolding formalism because of striking cancellations between an increase arising from the exclusion of the low-energy correlation and a shrinking arising from the renormalization of the frequency dependence. In the nondegenerate multiband materials such as FeSe and FeTe, the momentum dependent self-energy effects yield substantial modifications of the band structures and relative shifts of orbital-energy levels of the effective models, which may explain the stability of the bicollinear antiferromagnetic phase in FeTe as well as the experimental absence of the antiferromagnetic phase in FeSe.