Merge branch 'master' of git.irsamc.ups-tlse.fr:loos/SRGGW

Manuscript/SRGGW.bib

@@ -1,7 +1,7 @@
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-%% Created for Pierre-Francois Loos at 2023-03-10 11:18:15 +0100 
+%% Created for Pierre-Francois Loos at 2023-03-10 13:54:51 +0100 
 
 
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@@ -1101,12 +1101,12 @@
 	abstract = {The GW approximation (GWA) extends the well-known Hartree-Fock approximation (HFA) for the self-energy (exchange potential), by replacing the bare Coulomb potential v by the dynamically screened potential W, e.g. Vex = iGv is replaced by GW = iGW. Here G is the one-electron Green's function. The GWA like the HFA is self-consistent, which allows for solutions beyond perturbation theory, like say spin-density waves. In a first approximation, iGW is a sum of a statically screened exchange potential plus a Coulomb hole (equal to the electrostatic energy associated with the charge pushed away around a given electron). The Coulomb hole part is larger in magnitude, but the two parts give comparable contributions to the dispersion of the quasi-particle energy. The GWA can be said to describe an electronic polaron (an electron surrounded by an electronic polarization cloud), which has great similarities to the ordinary polaron (an electron surrounded by a cloud of phonons). The dynamical screening adds new crucial features beyond the HFA. With the GWA not only bandstructures but also spectral functions can be calculated, as well as charge densities, momentum distributions, and total energies. We will discuss the ideas behind the GWA, and generalizations which are necessary to improve on the rather poor GWA satellite structures in the spectral functions. We will further extend the GWA approach to fully describe spectroscopies like photoemission, x-ray absorption, and electron scattering. Finally we will comment on the relation between the GWA and theories for strongly correlated electronic systems. In collecting the material for this review, a number of new results and perspectives became apparent, which have not been published elsewhere.},
 	author = {Lars Hedin},
 	date-added = {2022-04-21 13:21:07 +0200},
-	date-modified = {2022-04-21 13:21:24 +0200},
+	date-modified = {2023-03-10 13:53:56 +0100},
 	doi = {10.1088/0953-8984/11/42/201},
 	journal = {J. Phys. Condens. Matter},
 	number = {42},
 	pages = {R489--R528},
-	title = {On correlation effects in electron spectroscopies and the$\less$i$\greater${GW}$\less$/i$\greater$approximation},
+	title = {On correlation effects in electron spectroscopies and the {{GW}} approximation},
 	volume = {11},
 	year = 1999,
 	bdsk-url-1 = {https://doi.org/10.1088/0953-8984/11/42/201}}
@@ -1803,13 +1803,13 @@
 	abstract = {A novel approach to the investigation of correlation effects in the electronic structure of magnetic crystals which takes into account a frequency dependence of the self-energy (the so-called `LDA++ approach') is developed. The fluctuation-exchange approximation is generalized to the spin-polarized multi-band case and a local version of it is proposed. As an example, we calculate the electronic quasiparticle spectrum of ferromagnetic iron. It is shown that the Fermi-liquid description of the bands near the Fermi level is reasonable, while the quasiparticle states beyond approximately the 1 eV range are strongly damped, in agreement with photoemission data. The result of the spin-polarized thermoemission experiment is explained satisfactorily. The problem of satellite structure is discussed.},
 	author = {M I Katsnelson and A I Lichtenstein},
 	date-added = {2021-11-03 15:06:54 +0100},
-	date-modified = {2021-11-03 15:08:06 +0100},
+	date-modified = {2023-03-10 13:54:45 +0100},
 	doi = {10.1088/0953-8984/11/4/011},
 	journal = {J. Phys. Condens. Matter},
 	month = {jan},
 	number = {4},
 	pages = {1037--1048},
-	title = {{LDA}$\mathplus$$\mathplus$ approach to the electronic structure of magnets: correlation effects in iron},
+	title = {{{LDA++}} approach to the electronic structure of magnets: correlation effects in iron},
 	volume = {11},
 	year = 1999,
 	bdsk-url-1 = {https://doi.org/10.1088/0953-8984/11/4/011}}

Manuscript/SRGGW.tex

@@ -735,7 +735,7 @@ In addition, the plateau is reached for larger values of $s$ in comparison to Fi
 Now turning to lithium hydride, \ce{LiH} (see middle panel of Fig.~\ref{fig:fig4}), we see that the qs$GW$ IP is actually worse than the fairly accurate HF value.
 However, SRG-qs$GW$ does not suffer from the same problem and improves slightly the accuracy as compared to HF.
 
-Finally, we also consider the evolution with respect to $s$ of the principal EA of \ce{F2} displayed in the right panel of Fig.~\ref{fig:fig4}.
+Finally, we also consider the evolution with respect to $s$ of the principal EA of \ce{F2} that is displayed in the right panel of Fig.~\ref{fig:fig4}.
 The HF value is largely underestimating the $\Delta$CCSD(T) reference.
 Performing a qs$GW$ calculation on top of it brings a quantitative improvement by reducing the error from \SI{-2.03}{\eV} to \SI{-0.24}{\eV}.
 The SRG-qs$GW$ EA (absolute) error is monotonically decreasing from the HF value at $s=0$ to an error close to the qs$GW$ one at $s\to\infty$.
@@ -768,7 +768,7 @@ The SRG-qs$GW$ EA (absolute) error is monotonically decreasing from the HF value
 %%% %%% %%% %%%
 
 Table \ref{tab:tab1} shows the principal IP of the 50 molecules considered in this work computed at various levels of theory.
-As mentioned previously, the HF approximation overestimates the IPs with a mean signed error (MSE) of \SI{0.56}{\eV} and a mean absolute error (MAE) of \SI{0.69}{\eV}.
+As previously mentioned, the HF approximation overestimates the IPs with a mean signed error (MSE) of \SI{0.56}{\eV} and a mean absolute error (MAE) of \SI{0.69}{\eV}.
 Performing a $G_0W_0$ calculation on top of this mean-field starting point, $G_0W_0$@HF, reduces by more than a factor two the MSE and MAE, \SI{0.29}{\eV} and \SI{0.33}{\eV}, respectively.
 However, there are still outliers with large errors. 
 For example, the IP of \ce{N2} is overestimated by \SI{1.56}{\eV}, a large discrepancy that is due to the HF starting point.