loos/SRGGW
2
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

update si

Browse Source
This commit is contained in:
Antoine Marie 2023-06-08 10:05:29 +02:00
parent 16ec190470
commit bbe39d59a5
3 changed files with 6 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
Manuscript/SRGGW.tex
View File

@ -67,7 +67,7 @@
\title{A similarity renormalization group approach to Green's function methods} \title{A similarity renormalization group approach to Green's function methods}
\author{Antoine \surname{Marie}} \author{Antoine \surname{Marie}\textsuperscript{*}}
\email{amarie@irsamc.ups-tlse.fr} \email{amarie@irsamc.ups-tlse.fr}
\affiliation{\LCPQ} \affiliation{\LCPQ}
@ -312,7 +312,7 @@ In this work, we consider Wegner's canonical generator \cite{Wegner_1994}
which satisfies the following condition \cite{Kehrein_2006} which satisfies the following condition \cite{Kehrein_2006}
\begin{equation} \begin{equation}
\label{eq:derivative_trace} \label{eq:derivative_trace}
\textcolor{red}{\dv{s}\text{Tr}\left[ \bH^\text{od}(s)^\dagger \bH^\text{od}(s) \right] \leq 0.} \dv{s}\text{Tr}\left[ \bH^\text{od}(s)^\dagger \bH^\text{od}(s) \right] \leq 0.
\end{equation} \end{equation}
This implies that the matrix elements of the off-diagonal part decrease in a monotonic way throughout the transformation. This implies that the matrix elements of the off-diagonal part decrease in a monotonic way throughout the transformation.
Moreover, the coupling coefficients associated with the highest-energy determinants are removed first as we shall evidence in the perturbative analysis below. Moreover, the coupling coefficients associated with the highest-energy determinants are removed first as we shall evidence in the perturbative analysis below.
@ -636,10 +636,10 @@ Performing a bijective transformation of the form,
on the renormalized quasiparticle equation \eqref{eq:GW_renorm} reverses the situation and makes it possible to choose $t$ such that there is no intruder states in the dynamic part, hence removing discontinuities. on the renormalized quasiparticle equation \eqref{eq:GW_renorm} reverses the situation and makes it possible to choose $t$ such that there is no intruder states in the dynamic part, hence removing discontinuities.
Note that, after this transformation, the form of the regularizer is actually closely related to the SRG-inspired regularizer introduced by Monino and Loos in Ref.~\onlinecite{Monino_2022}. Note that, after this transformation, the form of the regularizer is actually closely related to the SRG-inspired regularizer introduced by Monino and Loos in Ref.~\onlinecite{Monino_2022}.
\textcolor{red}{The intruder-state-free dynamic part of the self-energy makes it possible to define SRG-$G_0W_0$ and SRG-ev$GW$ schemes. The intruder-state-free dynamic part of the self-energy makes it possible to define SRG-$G_0W_0$ and SRG-ev$GW$ schemes.
Although the manuscript focuses on SRG-qs$GW$, the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness. Although the manuscript focuses on SRG-qs$GW$, the performance of SRG-$G_0W_0$ and SRG-ev$GW$ are discussed in the {\SupInf} for the sake of completeness.
In a nutshell, the SRG regularization improves slightly the overall convergence properties of SRG-ev$GW$ without altering its performance. In a nutshell, the SRG regularization improves slightly the overall convergence properties of SRG-ev$GW$ without altering its performance.
Likewise, the statistical indicators for $G_0W_0$ and SRG-$G_0W_0$ are extremely close.} Likewise, the statistical indicators for $G_0W_0$ and SRG-$G_0W_0$ are extremely close.
%=================================================================% %=================================================================%
\section{Computational details} \section{Computational details}

4
Manuscript/si.tex
View File

@ -1,5 +1,5 @@
%\documentclass[aps,prb,reprint,showkeys,superscriptaddress]{revtex4-1} %\documentclass[aps,prb,reprint,showkeys,superscriptaddress]{revtex4-1}
\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress]{revtex4-1} \documentclass[reprint,noshowkeys,superscriptaddress]{revtex4-1}
\usepackage{bm,graphicx,tabularx,array,booktabs,dcolumn,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,siunitx,enumitem} \usepackage{bm,graphicx,tabularx,array,booktabs,dcolumn,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,siunitx,enumitem}
\usepackage[version=4]{mhchem} \usepackage[version=4]{mhchem}
\usepackage[utf8]{inputenc} \usepackage[utf8]{inputenc}
@ -107,7 +107,7 @@
%\title{Characterising state-specific CASSCF theory: Excited states, symmetry breaking, and unphysical solutions} %\title{Characterising state-specific CASSCF theory: Excited states, symmetry breaking, and unphysical solutions}
%\title{Exploring the CASSCF energy landscape: Excited states, symmetry breaking, and unphysical solutions} %\title{Exploring the CASSCF energy landscape: Excited states, symmetry breaking, and unphysical solutions}
\author{Antoine \surname{Marie}} \author{Antoine \surname{Marie} \textsuperscript{*} }
\email{amarie@irsamc.ups-tlse.fr} \email{amarie@irsamc.ups-tlse.fr}
\affiliation{\LCPQ} \affiliation{\LCPQ}

BIN
Manuscript/supporting.pdf
View File

Binary file not shown.