<i>Ab initio</i>procedure for constructing effective models of correlated materials with entangled band structure

Abstract

In a previous work [Phys. Rev. B 77, 085122 (2008)], a procedure for constructing low-energy models of electrons in solids was proposed. The procedure starts with dividing the Hilbert space into two subspaces: the low-energy part (``$d$ space'') and the rest of the space (``$r$ space''). The low-energy model is constructed for the $d$ space by eliminating the degrees of freedom of the $r$ space. The thus derived model contains the strength of electron correlation expressed by a partially screened Coulomb interaction, calculated in the constrained random-phase approximation (cRPA), where screening channels within the $d$ space, ${P}_{d}$, are subtracted. One conceptual problem of this established downfolding method is that for entangled bands it is not clear how to cut out the $d$ space and how to distinguish ${P}_{d}$ from the total polarization. Here, we propose a simple procedure to overcome this difficulty. The $d$ space is defined to be an isolated set of bands generated from a set of maximally localized Wannier basis, which consequently defines ${P}_{d}$. The $r$ subspace is constructed as the complementary space orthogonal to the $d$ subspace, resulting in two sets of completely disentangled bands. Using these disentangled bands, the effective parameters of the $d$ space are uniquely determined by the cRPA method. The method is successfully applied to $3d$ transition metals.