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Ab-initio procedure for effective models of correlated materials with entangled band structure
We present a first-principles method for deriving effective low-energy models
of electrons in solids having entangled band structure. The procedure starts
with dividing the Hilbert space into two subspaces, the low-energy part ("
space'') and the rest of the space (" space''). The low-energy model is
constructed for the space by eliminating the degrees of freedom of the
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 space, , are subtracted. One conceptual problem of this
established downfolding method is that for entangled bands it is not clear how
to cut out the space and how to distinguish from the total
polarization. Here, we propose a simple procedure to overcome this difficulty.
In our scheme, the subspace is cut out from the Hilbert space of the Kohn
Sham eigenfunctions with the help of a procedure to construct a localized
Wannier basis. The subspace is constructed as the complementary space
orthogonal to the subspace. After this disentanglement, becomes well
defined. Using the disentangled bands, the effective parameters are uniquely
determined in the cRPA. The method is successfully applied to 3 transition
metals.Comment: 14 pages, 4 figure
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