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Manuscript/SRGGW.tex
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@ -62,8 +62,8 @@
\begin{document} \begin{document}
% \title{A Similarity Renormalization Group Approach To Many-Body Perturbation Theory} \title{A similarity renormalization group approach to Green's function methods}
\title{Tackling The Intruder-State Problem In Many-Body Perturbation Theory: A Similarity Renormalization Group Approach/Perspective} %\title{Tackling The Intruder-State Problem In Many-Body Perturbation Theory: A Similarity Renormalization Group Approach/Perspective}
\author{Antoine \surname{Marie}} \author{Antoine \surname{Marie}}
\email{amarie@irsamc.ups-tlse.fr} \email{amarie@irsamc.ups-tlse.fr}
@ -74,7 +74,12 @@
\affiliation{\LCPQ} \affiliation{\LCPQ}
\begin{abstract} \begin{abstract}
Here comes the abstract. The family of Green's function methods based on the $GW$ approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems and its affordability.
Despite this, self-consistent versions still pose challenges in terms of convergence.
A recent study \href{https://doi.org/10.1063/5.0089317}{[J. Chem. Phys. 156, 231101 (2022)]} has linked these convergence issues to the intruder-state problem.
In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods.
The resulting SRG-based regularized self-energy significantly accelerates the convergence of self-consistent $GW$ methods.
Furthermore, it enables us to derive, from first principles, the expression of a new naturally Hermitian form of the static self-energy that can be employed in quasiparticle self-consistent $GW$ (qs$GW$) calculations.
%\bigskip %\bigskip
%\begin{center} %\begin{center}
% \boxed{\includegraphics[width=0.5\linewidth]{TOC}} % \boxed{\includegraphics[width=0.5\linewidth]{TOC}}
@ -101,7 +106,6 @@ The $GW$ method approximates the self-energy $\Sigma$ which relates the exact in
\end{equation} \end{equation}
where $1 = (\bx_1, t_1)$ is a composite coordinate gathering spin-space and time variables. where $1 = (\bx_1, t_1)$ is a composite coordinate gathering spin-space and time variables.
The self-energy encapsulates all the Hartree-exchange-correlation effects which are not taken into account in the reference system. The self-energy encapsulates all the Hartree-exchange-correlation effects which are not taken into account in the reference system.
%Throughout this manuscript the references are chosen to be the Hartree-Fock (HF) ones so that the self-energy only account for the missing correlation.
Approximating $\Sigma$ as the first-order term of its perturbative expansion with respect to the screened Coulomb potential $W$ yields the so-called $GW$ approximation \cite{Hedin_1965,Martin_2016} Approximating $\Sigma$ as the first-order term of its perturbative expansion with respect to the screened Coulomb potential $W$ yields the so-called $GW$ approximation \cite{Hedin_1965,Martin_2016}
\begin{equation} \begin{equation}
\label{eq:gw_selfenergy} \label{eq:gw_selfenergy}
@ -535,7 +539,7 @@ This transformation is done gradually starting from the states that have the lar
\centering \centering
\includegraphics[width=\linewidth]{fig1.pdf} \includegraphics[width=\linewidth]{fig1.pdf}
\caption{ \caption{
Add caption Functional form of the qs$GW$ self-energy (left) for $\eta = 1$ and the SRG-$GW$ self-energy (right) for $s = 1/(2\eta^2)$.
\label{fig:fig1}} \label{fig:fig1}}
\end{figure*} \end{figure*}
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