From f4a66f0596a4fde329aa20ec43e1854997a07020 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Thu, 13 Oct 2022 10:54:56 +0200 Subject: [PATCH] modifs Antoine --- CCvsMBPT.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/CCvsMBPT.tex b/CCvsMBPT.tex index 9d9a259..e6de5a4 100644 --- a/CCvsMBPT.tex +++ b/CCvsMBPT.tex @@ -454,7 +454,7 @@ Within the perturbative $GW$ scheme (commonly known as $G_0W_0$), the quasiparti \cite{Strinati_1980,Hybertsen_1985a,Hybertsen_1986,Godby_1988,Linden_1988,Northrup_1991,Blase_1994,Rohlfing_1995,Shishkin_2007} Partial self-consistency can be attained via the \textit{``eigenvalue''} self-consistent $GW$ (ev$GW$) \cite{Hybertsen_1986,Shishkin_2007,Blase_2011,Faber_2011,Rangel_2016,Gui_2018} or the quasiparticle self-consistent $GW$ (qs$GW$) \cite{Faleev_2004,vanSchilfgaarde_2006,Kotani_2007,Ke_2011,Kaplan_2016} schemes. -In the most general setting, the quasiparticle energies and their corresponding orbitals are obtained by diagonalizing the so-called non-linear and frequency-dependent quasiparticle equation +In the most general setting, the quasiparticle energies and their corresponding orbitals are obtained self-consistently by diagonalizing the so-called non-linear and frequency-dependent quasiparticle equation \begin{equation} \label{eq:GW} \qty[ \be{}{} + \bSig{}{\GW}\qty(\omega = \e{p}{\GW}) ] \SO{p}{\GW} = \e{p}{\GW} \SO{p}{\GW} @@ -470,7 +470,7 @@ where $\be{}{}$ is a diagonal matrix gathering the HF orbital energies and the e \end{equation} Because both the left- and right-hand sides of Eq.~\eqref{eq:GW} depend on $\e{p}{\GW}$, this equation has to be solved iteratively via a self-consistent procedure. -As shown by Bintrim and Berkelbach, \cite{Bintrim_2021} the frequency-dependent $GW$ equations can be recast as a larger set of frequency-independent equations, which reads in the Tamm-Dancoff approximation +As shown by Bintrim and Berkelbach, \cite{Bintrim_2021} the quasiparticle equation \eqref{eq:GW} can be recast as a larger set of linear and frequency-independent equations (that still needs to be solved self-consistently), which reads in the Tamm-Dancoff approximation \begin{equation} \label{eq:GWlin} \begin{pmatrix}