From b9c03a4cb2ba0920e4846801cf8dfffc36af43d3 Mon Sep 17 00:00:00 2001 From: pfloos Date: Thu, 11 May 2023 19:52:47 +0200 Subject: [PATCH] modifs in manuscript --- Manuscript/SRGGW.tex | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/Manuscript/SRGGW.tex b/Manuscript/SRGGW.tex index dd55bb9..9114579 100644 --- a/Manuscript/SRGGW.tex +++ b/Manuscript/SRGGW.tex @@ -207,7 +207,7 @@ with \end{subequations} and where \begin{equation} - \braket{pq}{rs} = \iint \frac{\textcolor{red}{\SO{p}^*(\bx_1) \SO{q}^*(\bx_2)}\SO{r}(\bx_1) \SO{s}(\bx_2) }{\abs{\br_1 - \br_2}} d\bx_1 d\bx_2 + \braket{pq}{rs} = \iint \frac{\SO{p}(\bx_1) \SO{q}(\bx_2)\SO{r}(\bx_1) \SO{s}(\bx_2) }{\abs{\br_1 - \br_2}} d\bx_1 d\bx_2 \end{equation} are bare two-electron integrals in the spin-orbital basis. @@ -633,11 +633,13 @@ Performing a bijective transformation of the form, e^{- \Delta s} &= 1-e^{-\Delta t}, \end{align} on the renormalized quasiparticle equation \eqref{eq:GW_renorm} reverses the situation and makes it possible to choose $t$ such that there is no intruder states in the dynamic part, hence removing discontinuities. - -\textcolor{red}{The intruder-state free dynamic part makes it possible to define a SRG-$G_0W_0$ and SRG-ev$GW$. -The main manuscript focus on SRG-qs$GW$ but the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness.} Note that, after this transformation, the form of the regularizer is actually closely related to the SRG-inspired regularizer introduced by Monino and Loos in Ref.~\onlinecite{Monino_2022}. +\textcolor{red}{The intruder-state-free dynamic part of the self-energy makes it possible to define SRG-$G_0W_0$ and SRG-ev$GW$ schemes. +Although the manuscript focuses on SRG-qs$GW$, the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness. +In a nutshell, the SRG regularization improves the overall convergence properties of SRG-ev$GW$ without altering its performance. +Likewise, the statistical indicators for $G_0W_0$ and SRG-$G_0W_0$ are extremely close.} + %=================================================================% \section{Computational details} \label{sec:comp_det}