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two minor corrections in conclusion

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Antoine Marie 2023-03-10 11:40:04 +01:00
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Manuscript/SRGGW.tex
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@ -919,7 +919,7 @@ The problems caused by intruder states in many-body perturbation theory are nume
SRG's central equation is the flow equation, which is usually solved numerically but can be solved analytically for low perturbation order. SRG's central equation is the flow equation, which is usually solved numerically but can be solved analytically for low perturbation order.
Applying this approach in the $GW$ context yields analytical renormalized expressions for the Fock matrix elements and the screened two-electron integrals. Applying this approach in the $GW$ context yields analytical renormalized expressions for the Fock matrix elements and the screened two-electron integrals.
These renormalized quantities lead to a renormalized $GW$ quasiparticle equation, referred to as SRG-$GW$, which is the main result of this work. These renormalized quantities lead to a regularized $GW$ quasiparticle equation, referred to as SRG-$GW$, which is the main result of this work.
By isolating the static component of SRG-$GW$, we obtain an alternative Hermitian and intruder-state-free self-energy that can be used in the context of qs$GW$ calculations. By isolating the static component of SRG-$GW$, we obtain an alternative Hermitian and intruder-state-free self-energy that can be used in the context of qs$GW$ calculations.
This new variant is called SRG-qs$GW$. This new variant is called SRG-qs$GW$.
@ -927,7 +927,7 @@ Additionally, we demonstrate how SRG-$GW$ can effectively resolve the discontinu
This provides a first-principles justification for the SRG-inspired regularizer proposed in Ref.~\onlinecite{Monino_2022}. This provides a first-principles justification for the SRG-inspired regularizer proposed in Ref.~\onlinecite{Monino_2022}.
We first study the flow parameter dependence of the SRG-qs$GW$ IPs for a few test cases. We first study the flow parameter dependence of the SRG-qs$GW$ IPs for a few test cases.
The results show that the IPs gradually evolve from the HF starting point at $s=0$ to a plateau value for $s\to\infty$ that is much closer to the CCSD(T) reference than the HF initial value. The results show that the IPs gradually evolve from the HF starting point at $s=0$ to a plateau value for $s\to\infty$ that is much closer to the $\Delta$CCSD(T) reference than the HF initial value.
For small values of the flow parameter, the SRG-qs$GW$ IPs are actually worse than their starting point. For small values of the flow parameter, the SRG-qs$GW$ IPs are actually worse than their starting point.
Therefore, it is advisable to use the largest possible value of $s$, similar to qs$GW$ calculations where one needs to use the smallest possible $\eta$ value. Therefore, it is advisable to use the largest possible value of $s$, similar to qs$GW$ calculations where one needs to use the smallest possible $\eta$ value.