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Pierre-Francois Loos 2022-10-19 09:22:14 +02:00
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CCvsMBPT.tex
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@ -441,6 +441,7 @@ At the CCSD level, for example, this is achieved by performing IP-EOM-CCSD \cite
Following the same philosophy, in BSE@$GW$, one performs first a $GW$ calculation (which corresponds to an approximate and simultaneous treatment of the IP and EA sectors up to 2h1p and 2p1h \cite{Lange_2018,Monino_2022}) in order to renormalize the one-electron energies (see Sec.~\ref{sec:GW} for more details). Following the same philosophy, in BSE@$GW$, one performs first a $GW$ calculation (which corresponds to an approximate and simultaneous treatment of the IP and EA sectors up to 2h1p and 2p1h \cite{Lange_2018,Monino_2022}) in order to renormalize the one-electron energies (see Sec.~\ref{sec:GW} for more details).
Then, a static BSE calculation is performed in the 1h1p sector with a two-body term dressed with correlation stemming from $GW$. Then, a static BSE calculation is performed in the 1h1p sector with a two-body term dressed with correlation stemming from $GW$.
The dynamical version of BSE [where the BSE kernel is explicitly treated as frequency-dependent in Eq.~\eqref{eq:BSE}] takes partially into account the 2h2p configurations. \cite{Strinati_1980,Strinati_1982,Strinati_1984,Strinati_1988,Rohlfing_2000,Romaniello_2009b,Loos_2020h,Authier_2020,Monino_2021,Bintrim_2022} The dynamical version of BSE [where the BSE kernel is explicitly treated as frequency-dependent in Eq.~\eqref{eq:BSE}] takes partially into account the 2h2p configurations. \cite{Strinati_1980,Strinati_1982,Strinati_1984,Strinati_1988,Rohlfing_2000,Romaniello_2009b,Loos_2020h,Authier_2020,Monino_2021,Bintrim_2022}
\titou{More equations and/or figures?}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Connection between $GW$ and CC} \section{Connection between $GW$ and CC}
@ -611,6 +612,7 @@ To determine the 2h1p and 2p1h amplitudes, $t_{ija,p}^{\text{2h1p}}$ and $t_{iab
t_{iab,p}^{\text{2p1h}} & \leftarrow t_{iab,p}^{\text{2p1h}} - \qty( \Delta_{iab,p}^{\text{2p1h}} )^{-1} r_{iab,p}^{\text{2p1h}} t_{iab,p}^{\text{2p1h}} & \leftarrow t_{iab,p}^{\text{2p1h}} - \qty( \Delta_{iab,p}^{\text{2p1h}} )^{-1} r_{iab,p}^{\text{2p1h}}
\end{align} \end{align}
\end{subequations} \end{subequations}
\titou{Maybe analyze further these equations and mention that we obtain an eigensystem, not an energy like in CC?}
The quasiparticle energies $\e{p}{GW}$ are thus provided by the eigenvalues of $\be{}{} + \bSig{}{\GW}$, where The quasiparticle energies $\e{p}{GW}$ are thus provided by the eigenvalues of $\be{}{} + \bSig{}{\GW}$, where
\begin{equation} \begin{equation}