From e51468a9dcbde011811bd1bff6462d657a1c6ebf Mon Sep 17 00:00:00 2001 From: Antoine MARIE Date: Fri, 12 May 2023 08:28:38 +0200 Subject: [PATCH] save before pull --- Manuscript/SRGGW.tex | 15 +-------------- 1 file changed, 1 insertion(+), 14 deletions(-) diff --git a/Manuscript/SRGGW.tex b/Manuscript/SRGGW.tex index dd55bb9..627cfe8 100644 --- a/Manuscript/SRGGW.tex +++ b/Manuscript/SRGGW.tex @@ -364,20 +364,7 @@ Indeed, the $GW$ quasiparticle equation is equivalent to the diagonalization of % \boldsymbol{\epsilon}, \end{equation} %where $\boldsymbol{\epsilon}$ is a diagonal matrix collecting the quasiparticle and satellite energies, -where the 2h1p and 2p1h matrix elements are -\begin{subequations} - \begin{align} - C^\text{2h1p}_{i\nu,j\mu} & = \left(\epsilon_i - \Omega_\nu\right)\delta_{ij}\delta_{\nu\mu}, - \\ - C^\text{2p1h}_{a\nu,b\mu} & = \left(\epsilon_a + \Omega_\nu\right)\delta_{ab}\delta_{\nu\mu}, - \end{align} -\end{subequations} -and the corresponding coupling blocks read [see Eq.~(\ref{eq:GW_sERI})] -\begin{align} - W^\text{2h1p}_{p,i\nu} & = W_{pi}^{\nu}, - & - W^\text{2p1h}_{p,a\nu} & = W_{pa}^{\nu}. -\end{align} + The usual $GW$ non-linear equation can be obtained by applying L\"owdin partitioning technique \cite{Lowdin_1963} to Eq.~\eqref{eq:GWlin} yielding \cite{Bintrim_2021} \begin{equation} \begin{split}