Historically, the GW approach was put forward by Hedin as the simplest approximation to the so-called Hedin equations. In Section 2, we will derive these Hedin equations from a Feynman-diagrammatical point of view. Section 3.1 shows how GW arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation D $Γ$ A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.Historically, the GW approach was put forward by Hedin as the simplest approximation to the so-called Hedin equations. In Section 2, we will derive these Hedin equations from a Feynman-diagrammatical point of view. Section 3.1 shows how GW arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation D$Γ$A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.

arXiv:1109.3972Sep 19, 20118 citations

A Diagrammatic Route to Multi-Reference GW for Strongly Correlated Molecules

Yuqi Wang, Wei‐Hai Fang, Zhendong Li

The GW approximation is a cornerstone of many-body perturbation theory for computing single-particle excitations, yet it can fail qualitatively in strongly correlated systems where the single-reference picture becomes inadequate. To overcome this limitation, we develop a diagrammatic route to multi-reference GW (MR-GW) from an interacting active-space reference, treating strong correlation nonperturbatively and the residual interaction through dynamical screening at the multi-reference random phase approximation level. Because the conventional diagrammatic self-energy expansion no longer applies, we define a practical one-shot MR-GW approximation within a generalized diagrammatic framework, recovering standard GW as a special case. Applications to prototypical correlated atoms and molecules show that the interacting active-space reference captures multiconfigurational satellite structures poorly described by single-reference GW, while dynamical screening generally improves the satellite energies as well as the leading ionization and electron-attachment energies. This work opens a diagrammatic route to Green's-function methods that combine nonperturbative strong correlation with dynamical screening.The GW approximation is a cornerstone of many-body perturbation theory for computing single-particle excitations, yet it can fail qualitatively in strongly correlated systems where the single-reference picture becomes inadequate. To overcome this limitation, we develop a diagrammatic route to multi-reference GW (MR-GW) from an interacting active-space reference, treating strong correlation nonperturbatively and the residual interaction through dynamical screening at the multi-reference random phase approximation level. Because the conventional diagrammatic self-energy expansion no longer applies, we define a practical one-shot MR-GW approximation within a generalized diagrammatic framework, recovering standard GW as a special case. Applications to prototypical correlated atoms and molecules show that the interacting active-space reference captures multiconfigurational satellite structures poorly described by single-reference GW, while dynamical screening generally improves the satellite energies as well as the leading ionization and electron-attachment energies. This work opens a diagrammatic route to Green's-function methods that combine nonperturbative strong correlation with dynamical screening.

arXiv:2604.16013Apr 17, 20260 citations

The GW Approximation

WORLD SCIENTIFIC eBooksMar 23, 20250 citations

Diagrammatic Monte Carlo and GW Approximation for Jellium and Hydrogen Chain

Kris Van Houcke, I. S. Tupitsyn, Nikolay V. Prokof'ev

Springer eBooksJan 1, 20180 citations

Application of the GW Approximation to Trans

Elana Chris Ethridge

Jan 1, 19930 citations

Γ

A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.