### Abstract

In a previous work, 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, Pd, 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 Pd 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 Pd. 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.

Original language | English |
---|---|

Article number | 155134 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 80 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2009 Oct 27 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*80*(15), [155134]. https://doi.org/10.1103/PhysRevB.80.155134

**Ab initio procedure for constructing effective models of correlated materials with entangled band structure.** / Miyake, Takashi; Aryasetiawan, Ferdi; Imada, Masatoshi.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 80, no. 15, 155134. https://doi.org/10.1103/PhysRevB.80.155134

}

TY - JOUR

T1 - Ab initio procedure for constructing effective models of correlated materials with entangled band structure

AU - Miyake, Takashi

AU - Aryasetiawan, Ferdi

AU - Imada, Masatoshi

PY - 2009/10/27

Y1 - 2009/10/27

N2 - In a previous work, 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, Pd, 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 Pd 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 Pd. 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.

AB - In a previous work, 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, Pd, 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 Pd 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 Pd. 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.

UR - http://www.scopus.com/inward/record.url?scp=71449127106&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71449127106&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.80.155134

DO - 10.1103/PhysRevB.80.155134

M3 - Article

AN - SCOPUS:71449127106

VL - 80

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 15

M1 - 155134

ER -