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fix merge conflict

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Antoine Marie 2023-03-03 11:56:36 +01:00
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@ -267,7 +267,8 @@ If it is not the case, the self-consistent qs$GW$ scheme inevitably oscillates b
The satellites causing convergence problems are the above-mentioned intruder states. \cite{Monino_2022} The satellites causing convergence problems are the above-mentioned intruder states. \cite{Monino_2022}
One can deal with them by introducing \textit{ad hoc} regularizers. One can deal with them by introducing \textit{ad hoc} regularizers.
For example, the $\ii\eta$ term in the denominators of Eq.~\eqref{eq:GW_selfenergy}, sometimes referred to as a broadening parameter linked to the width of the quasiparticle peak, is similar to the usual imaginary-shift regularizer employed in various other theories plagued by the intruder-state problem. \cite{Surjan_1996,Forsberg_1997,Monino_2022,Battaglia_2022}. For example, the $\ii\eta$ term in the denominators of Eq.~\eqref{eq:GW_selfenergy}, sometimes referred to as a broadening parameter linked to the width of the quasiparticle peak, is similar to the usual imaginary-shift regularizer employed in various other theories plagued by the intruder-state problem. \cite{Surjan_1996,Forsberg_1997,Monino_2022,Battaglia_2022}.
However, this $\eta$ parameter stems from a regularization of the convolution that yields the self-energy and should theoretically be set to zero. \cite{Martin_2016}
However, this $\eta$ parameter is required to define the Fourier transformation between time and energy representation and should theoretically be set to zero. \cite{Martin_2016}
Several other regularizers are possible \cite{Stuck_2013,Rostam_2017,Lee_2018a,Evangelista_2014b,Shee_2021,Coveney_2023} and, in particular, it was shown in Ref.~\onlinecite{Monino_2022} that a regularizer inspired by the SRG had some advantages over the imaginary shift. Several other regularizers are possible \cite{Stuck_2013,Rostam_2017,Lee_2018a,Evangelista_2014b,Shee_2021,Coveney_2023} and, in particular, it was shown in Ref.~\onlinecite{Monino_2022} that a regularizer inspired by the SRG had some advantages over the imaginary shift.
Nonetheless, it would be more rigorous, and more instructive, to obtain this regularizer from first principles by applying the SRG formalism to many-body perturbation theory. Nonetheless, it would be more rigorous, and more instructive, to obtain this regularizer from first principles by applying the SRG formalism to many-body perturbation theory.
This is one of the aims of the present work. This is one of the aims of the present work.