Ab initio procedure for constructing effective models of correlated materials with entangled band structure

By T. Miyake, F. Aryasetiawan, M. Imada. 2009

138 citations recorded by the source corpus.

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 ("$d$ 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. In our scheme, the $d$ 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 $r$ subspace is constructed as the complementary space orthogonal to the $d$ subspace. After this disentanglement, $P_d$ becomes well defined. Using the disentangled bands, the effective parameters are uniquely determined in the cRPA. The method is successfully applied to 3$d$ transition metals.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/2487a1bdb8a0633f9d55174d4015c21afe6f1549

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, methodology): “In such cases a downfolding procedure can be applied (Miyake, Aryasetiawan, and Imada, 2009) in which the low-energy effective model contains a Hubbard U that depends on the screening from electrons in delocalized environmental orbitals.”
Reformulation of DFT + U as a pseudohybrid hubbard density functional for accelerated materials discovery (2015, background): “Recently, maximally localized Wannier functions (MLWF), an invariant choice suitable for plane-wave calculations, have also been employed [31,39].”
Maximally-localized Wannier Functions: Theory and Applications (2011, background): “…al., 1991; Dederichs et al., 1984; McMahan et al., 1990; Nakamura et al., 2006), within the random phase approximation (Aryasetiawan et al., 2004; Miyake et al., 2009; Solovyev and Imada, 2005; Springer and Aryasetiawan, 1998), or by direct calculation of the matrix elements of a suitable…”