add bib

Manuscript/EPAWTFT.bbl

@@ -6,7 +6,7 @@
 %Control: page (0) single
 %Control: year (1) truncated
 %Control: production of eprint (0) enabled
-\begin{thebibliography}{158}%
+\begin{thebibliography}{160}%
 \makeatletter
 \providecommand \@ifxundefined [1]{%
  \@ifx{#1\undefined}
@@ -1403,9 +1403,8 @@
   \BibitemOpen
   \bibfield  {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont
   {Shanks}},\ }\href {\doibase https://doi.org/10.1002/sapm19553411} {\bibfield
-   {journal} {\bibinfo  {journal} {Journal of Mathematics and Physics}\
-  }\textbf {\bibinfo {volume} {34}},\ \bibinfo {pages} {1} (\bibinfo {year}
-  {1955})}\BibitemShut {NoStop}%
+   {journal} {\bibinfo  {journal} {J. Math. Phys.}\ }\textbf {\bibinfo {volume}
+  {34}},\ \bibinfo {pages} {1} (\bibinfo {year} {1955})}\BibitemShut {NoStop}%
 \bibitem [{\citenamefont {Surj{\'a}n}\ and\ \citenamefont
   {Szabados}(2000)}]{Surjan_2000}%
   \BibitemOpen
@@ -1513,4 +1512,26 @@
   {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo
   {volume} {124}},\ \bibinfo {pages} {243001} (\bibinfo {year}
   {2020})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Smith}\ \emph {et~al.}(2016)\citenamefont {Smith},
+  \citenamefont {{Pribram-Jones}},\ and\ \citenamefont {Burke}}]{Smith_2016}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~C.}\ \bibnamefont
+  {Smith}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
+  {{Pribram-Jones}}}, \ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
+  {Burke}},\ }\href {\doibase 10.1103/PhysRevB.93.245131} {\bibfield  {journal}
+  {\bibinfo  {journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {93}},\
+  \bibinfo {pages} {245131} (\bibinfo {year} {2016})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Smith}\ \emph {et~al.}()\citenamefont {Smith},
+  \citenamefont {Sagredo},\ and\ \citenamefont {Burke}}]{Smith_2018}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
+  {Smith}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Sagredo}}, \
+  and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Burke}},\ }in\ \href
+  {\doibase 10.1007/978-981-10-5651-2_11} {\emph {\bibinfo {booktitle}
+  {Frontiers of Quantum Chemistry}}},\ \bibinfo {editor} {edited by\ \bibinfo
+  {editor} {\bibfnamefont {M.}~\bibnamefont {W{\'o}jcik}}, \bibinfo {editor}
+  {\bibfnamefont {H.}~\bibnamefont {Nakatsuji}}, \bibinfo {editor}
+  {\bibfnamefont {B.}~\bibnamefont {Kirtman}}, \ and\ \bibinfo {editor}
+  {\bibfnamefont {Y.}~\bibnamefont {Ozaki}}}\ (\bibinfo  {publisher} {Springer,
+  Singapore})\BibitemShut {NoStop}%
 \end{thebibliography}%

Manuscript/EPAWTFT.bib

@@ -1,13 +1,35 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2020-12-02 21:47:07 +0100 
+%% Created for Pierre-Francois Loos at 2020-12-02 21:56:11 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@incollection{Smith_2018,
+	author = {J.C. Smith and F. Sagredo and K. Burke},
+	booktitle = {Frontiers of Quantum Chemistry},
+	date-added = {2020-12-02 21:52:16 +0100},
+	date-modified = {2020-12-02 21:56:11 +0100},
+	doi = {10.1007/978-981-10-5651-2_11},
+	editor = {M. W{\'o}jcik and H. Nakatsuji and B. Kirtman and Y. Ozaki},
+	publisher = {Springer, Singapore},
+	title = {Warming Up Density Functional Theory}}
+
+@article{Smith_2016,
+	author = {Smith, J. C. and {Pribram-Jones}, A. and Burke, K.},
+	date-added = {2020-12-02 21:49:33 +0100},
+	date-modified = {2020-12-02 21:49:42 +0100},
+	doi = {10.1103/PhysRevB.93.245131},
+	journal = {Phys. Rev. B},
+	pages = {245131},
+	title = {Exact Thermal Density Functional Theory for a Model System: {{Correlation}} Components and Accuracy of the Zero-Temperature Exchange-Correlation Approximation},
+	volume = {93},
+	year = {2016},
+	Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.93.245131}}
+
 @article{Shanks_1955,
 	abstract = {This paper discusses a family of non-linear sequence-to-sequence transformations designated as ek, ekm, {\~e}k, and ed. A brief history of the transforms is related and a simple motivation for the transforms is given. Examples are given of the application of these transformations to divergent and slowly convergent sequences. In particular the examples include numerical series, the power series of rational and meromorphic functions, and a wide variety of sequences drawn from continued fractions, integral equations, geometry, fluid mechanics, and number theory. Theorems are proven which show the effectiveness of the transformations both in accelerating the convergence of (some) slowly convergent sequences and in inducing convergence in (some) divergent sequences. The essential unity of these two motives is stressed. Theorems are proven which show that these transforms often duplicate the results of well-known, but specialized techniques. These special algorithms include Newton's iterative process, Gauss's numerical integration, an identity of Euler, the Pad{\'e} Table, and Thiele's reciprocal differences. Difficulties which sometimes arise in the use of these transforms such as irregularity, non-uniform convergence to the wrong answer, and the ambiguity of multivalued functions are investigated. The concepts of antilimit and of the spectra of sequences are introduced and discussed. The contrast between discrete and continuous spectra and the consequent contrasting response of the corresponding sequences to the e1 transformation is indicated. The characteristic behaviour of a semiconvergent (asymptotic) sequence is elucidated by an analysis of its spectrum into convergent components of large amplitude and divergent components of small amplitude.},
 	author = {Shanks, Daniel},

Manuscript/EPAWTFT.tex

@@ -1741,7 +1741,7 @@ However, it is worth mentioning that the construction of these approximants requ
 The Shanks transformation presented in Sec.~\ref{sec:Shanks} can, in some cases, alleviate this issue.
 
 Most of the physical concepts and mathematical tools reviewed in the present manuscript has been illustrated on the symmetric (or asymmetric in one occasion) Hubbard dimer at half-filling.
-Although extremely simple, this clearly illustrates the obvious versatility of the Hubbard model to understand perturbation theory as well as other concepts such as Kohn-Sham density-functional theory (DFT), \cite{Carrascal_2015} linear-response theory, \cite{Carrascal_2018} many-body perturbation theory, \cite{Romaniello_2009,Romaniello_2012,DiSabatino_2015,Tarantino_2017}, DFT for ensembles, \cite{Deur_2017,Deur_2018,Senjean_2018,Sagredo_2018,Fromager_2020} and many others.
+Although extremely simple, this clearly illustrates the obvious versatility of the Hubbard model to understand perturbation theory as well as other concepts such as Kohn-Sham density-functional theory (DFT), \cite{Carrascal_2015} linear-response theory, \cite{Carrascal_2018} many-body perturbation theory, \cite{Romaniello_2009,Romaniello_2012,DiSabatino_2015,Tarantino_2017}, DFT for ensembles, \cite{Deur_2017,Deur_2018,Senjean_2018,Sagredo_2018,Fromager_2020} thermal DFT, \cite{Smith_2016,Smith_2018} and many others.
 We believe that the Hubbard dimer could then be used for further developments and comprehension around perturbation theory.
 
 As a concluding remark and from a broader point of view, the present work shows that our understanding of the singularity structure of the energy is still incomplete.