Derivation of Static Low-Energy Effective Models by ab initio Downfolding Method without Double Counting of Coulomb Correlations: Application to SrVO3, 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 constrained self-energy corrections defined by the sum of the contribution from eliminated high-energy degrees of freedom, Sigma H and that from the frequency-dependent part of the partially screened interaction, Delta Sigma L. We apply the formalism to SrVO3 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 of Sigma H and Delta Sigma L. In SrVO3, the resultant bandwidth of the effective low-energy model is 2.56 eV (in comparison to LDA: 2.58 eV, full GW approximation: 2.19 eV). However, in the non-degenerate multi-band 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. The FeSe model indicates a substantial downward shift of the x2-y2 orbital level, which may lead to an increase in the filling of the x2-y2 orbital above half filling. It suggests a destruction of the orbital selective Mott phase of the x2-y2 orbital in agreement with the experimental absence of the antiferromagnetic phase.