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arXiv:2410.19579 · Physical review. B./Physical review. B

Self-consistent G W + extended dynamical mean field theory for semiconductors and insulators

Viktor Christiansson, Francesco Petocchi, Philipp Werner

Published Jun 12, 2026• 0 citations
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Abstract

Theoretical studies of semiconductors and band insulators are usually based on variants of the $GW$ method without full self-consistency, like single-shot $G^0W^0$ or quasiparticle self-consistent $GW$. Fully self-consistent $GW$ provides a poor description of the gap size and electronic structure due to the lack of vertex corrections. While it is hard to predict at which order corrections can be neglected, local vertex corrections to all orders can be consistently included by combining $GW$ with extended dynamical mean field theory (EDMFT). Here, we show that \textit{ab initio} multitier $GW$+EDMFT calculations, which achieve full self-consistency in a suitably defined low-energy space, provide an accurate description of semiconductors and band insulators, comparable to the established methods which are typically used for this class of materials. Our results demonstrate that the range of applicability of $GW$+EDMFT extends to weakly correlated systems, and they imply that despite the weak correlations, local vertex corrections are an important ingredient in the diagrammatic treatment of semiconductors and band insulators.

DOI
10.1103/3p68-9flm

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Theoretical studies of semiconductors and band insulators are usually based on variants of the GWGWGW method without full self-consistency, like single-shot G0W0G^0W^0G0W0 or quasiparticle self-consistent GWGWGW. Fully self-consistent GWGWGW provides a poor description of the gap size and electronic structure due to the lack of vertex corrections. While it is hard to predict at which order corrections can be neglected, local vertex corrections to all orders can be consistently included by combining GWGWGW with extended dynamical mean field theory (EDMFT). Here, we show that \textit{ab initio} multitier GWGWGW+EDMFT calculations, which achieve full self-consistency in a suitably defined low-energy space, provide an accurate description of semiconductors and band insulators, comparable to the established methods which are typically used for this class of materials. Our results demonstrate that the range of applicability of GWGWGW+EDMFT extends to weakly correlated systems, and they imply that despite the weak correlations, local vertex corrections are an important ingredient in the diagrammatic treatment of semiconductors and band insulators.
ComDMFT is a parallel computational package designed to study the electronic structure of correlated quantum materials from first principles. Our approach is based on the combination of first-principles methods and dynamical mean field theories. In version 2.0, we implemented fully-diagrammatic GW+EDMFT from first-principles. In this approach, correlated electrons are treated within full GW+EDMFT and the rest are treated within full-GW, seamlessly. This implementation enables the electronic structure calculation of quantum materials with weak, intermediate, and strong electron correlation without prior knowledge of the degree of electron correlation.
Accidental accuracy and vertex corrections in GWGWGW: Exact benchmarks for the extended Hubbard model
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