From 668b2f1bdb1f39bb49c777b4ac1878b2ad800dd0 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 27 Nov 2020 20:55:21 +0100 Subject: [PATCH] forgotten references --- Manuscript/EPAWTFT.bbl | 163 +++++++++-------------------------------- Manuscript/EPAWTFT.bib | 32 +++++++- Manuscript/EPAWTFT.tex | 4 +- 3 files changed, 65 insertions(+), 134 deletions(-) diff --git a/Manuscript/EPAWTFT.bbl b/Manuscript/EPAWTFT.bbl index 5529caa..87da465 100644 --- a/Manuscript/EPAWTFT.bbl +++ b/Manuscript/EPAWTFT.bbl @@ -6,7 +6,7 @@ %Control: page (0) single %Control: year (1) truncated %Control: production of eprint (0) enabled -\begin{thebibliography}{141}% +\begin{thebibliography}{131}% \makeatletter \providecommand \@ifxundefined [1]{% \@ifx{#1\undefined} @@ -1060,25 +1060,6 @@ {journal} {J. Chem. 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Phys.}\ }\textbf {\bibinfo {volume} {43}},\ \bibinfo {pages} {479} (\bibinfo {year} {1971})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Sergeev}\ \emph {et~al.}(2005)\citenamefont + {Sergeev}, \citenamefont {Goodson}, \citenamefont {Wheeler},\ and\ + \citenamefont {Allen}}]{Sergeev_2005}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~V.}\ \bibnamefont + {Sergeev}}, \bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont + {Goodson}}, \bibinfo {author} {\bibfnamefont {S.~E.}\ \bibnamefont + {Wheeler}}, \ and\ \bibinfo {author} {\bibfnamefont {W.~D.}\ \bibnamefont + {Allen}},\ }\href {\doibase 10.1063/1.1991854} {\bibfield {journal} + {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {123}},\ + \bibinfo {pages} {064105} (\bibinfo {year} {2005})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Goodson}\ and\ \citenamefont {Sergeev}(2004)}]{Goodson_2004}% \BibitemOpen @@ -1101,6 +1093,28 @@ {\bibinfo {booktitle} {Adv. Quantum Chem.}}},\ Vol.~\bibinfo {volume} {47}\ (\bibinfo {publisher} {Academic Press},\ \bibinfo {year} {2004})\ pp.\ \bibinfo {pages} {193--208}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Goodson}(2000{\natexlab{a}})}]{Goodson_2000a}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont + {Goodson}},\ }\href {\doibase 10.1063/1.481044} {\bibfield {journal} + {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {112}},\ + \bibinfo {pages} {4901} (\bibinfo {year} {2000}{\natexlab{a}})}\BibitemShut + {NoStop}% +\bibitem [{\citenamefont {Goodson}(2000{\natexlab{b}})}]{Goodson_2000b}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont + {Goodson}},\ }\href {\doibase 10.1063/1.1318740} {\bibfield {journal} + {\bibinfo {journal} {J. Chem. 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C.: Solid State Phys.}\ }\textbf {\bibinfo {volume} {18}},\ \bibinfo {pages} {3297} (\bibinfo {year} {1985})}\BibitemShut {NoStop}% -\bibitem [{\citenamefont {Goodson}(2000)}]{Goodson_2000}% - \BibitemOpen - \bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont - {Goodson}},\ }\href {\doibase 10.1063/1.481044} {\bibfield {journal} - {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {112}},\ - \bibinfo {pages} {4901} (\bibinfo {year} {2000})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Surj{\'a}n}\ and\ \citenamefont {Szabados}(2000)}]{Surjan_2000}% \BibitemOpen diff --git a/Manuscript/EPAWTFT.bib b/Manuscript/EPAWTFT.bib index e5e0a48..9f7aa9c 100644 --- a/Manuscript/EPAWTFT.bib +++ b/Manuscript/EPAWTFT.bib @@ -1,13 +1,39 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-11-25 22:26:55 +0100 +%% Created for Pierre-Francois Loos at 2020-11-27 20:55:11 +0100 %% Saved with string encoding Unicode (UTF-8) +@article{Kais_2006, + abstract = {Finite size scaling for calculations of the critical parameters of the few-body Schr{\"o}dinger equation is based on taking the number of elements in a complete basis set as the size of the system. We show in an analogy with Yang and Lee theorem, which states that singularities of the free energy at phase transitions occur only in the thermodynamic limit, that singularities in the ground state energy occur only in the infinite complete basis set limit. To illustrate this analogy in the complex-parameter space, we present calculations for Yukawa type potential, and a Coulomb type potential for two-electron atoms.}, + author = {Sabre Kais and Craig Wenger and Qi Wei}, + date-added = {2020-11-27 20:54:34 +0100}, + date-modified = {2020-11-27 20:55:08 +0100}, + doi = {https://doi.org/10.1016/j.cplett.2006.03.035}, + journal = {Chem. Phys. Lett.}, + pages = {45 - 49}, + title = {Quantum criticality at the infinite complete basis set limit: A thermodynamic analog of the Yang and Lee theorem}, + volume = {423}, + year = {2006}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261406003897}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2006.03.035}} + +@article{Goodson_2000b, + author = {Goodson,David Z.}, + date-added = {2020-11-27 20:42:57 +0100}, + date-modified = {2020-11-27 20:43:12 +0100}, + doi = {10.1063/1.1318740}, + journal = {J. Chem. Phys.}, + pages = {6461-6464}, + title = {A summation procedure that improves the accuracy of the fourth-order Mo/ller--Plesset perturbation theory}, + volume = {113}, + year = {2000}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1318740}} + @article{Pavlyukh_2017, author = {Y. Pavlyukh}, date-added = {2020-11-25 22:26:26 +0100}, @@ -33,10 +59,10 @@ Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.99.075149}, Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.99.075149}} -@article{Goodson_2000, +@article{Goodson_2000a, author = {Goodson,David Z.}, date-added = {2020-11-25 10:05:02 +0100}, - date-modified = {2020-11-25 10:05:17 +0100}, + date-modified = {2020-11-27 20:42:22 +0100}, doi = {10.1063/1.481044}, journal = {J. Chem. Phys.}, pages = {4901-4909}, diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index db2858c..f08a64b 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -1179,7 +1179,7 @@ To further develop the link between the critical point and types of MP convergen the relationship with the location of the dominant singularity that controls the radius of convergence.\cite{Goodson_2004}. They demonstrated that the dominant singularity in class A corresponds to a dominant EP with a positive real component, with the magnitude of the imaginary component controlling the oscillations in the signs of the MP -term.\cite{Goodson_2000a,Goodson200b} +term.\cite{Goodson_2000a,Goodson_2000b} In contrast, class B systems correspond to a dominant singularity on the negative real $\lambda$ axis representing the MP critical point. The divergence of class B systems, which contain closely spaced electrons (\eg, \ce{F-}), can then be understood as the @@ -1383,7 +1383,7 @@ and substituting $E(\lambda$) by its $n$th-order expansion and the polynomials b A quadratic approximant, characterised by the label $[d_P/d_Q,d_R]$, generates, by construction, $n_\text{bp} = \max(2d_p,d_q+d_r)$ branch points at the roots of the polynomial $P^2(\lambda) - 4 Q(\lambda) R(\lambda)$. The diagonal sequence of quadratic approximant, \ie, $[0/0,0]$, $[1/0,0]$, $[1/0,1]$, $[1/1,1]$, $[2/1,1]$, is of particular interest. Note that, by construction, a quadratic approximant has only two branches which hampers the faithful description of more complicated singularity structures. -As shown in Ref.~\onlinecite{Goodson_2000}, quadratic approximants provide convergent results in the most divergent cases considered by Olsen and collaborators \cite{Christiansen_1996,Olsen_1996} and Leininger \etal \cite{Leininger_2000} +As shown in Ref.~\onlinecite{Goodson_2000a}, quadratic approximants provide convergent results in the most divergent cases considered by Olsen and collaborators \cite{Christiansen_1996,Olsen_1996} and Leininger \etal \cite{Leininger_2000} For the RMP series of the Hubbard dimer, the $[0/0,0]$ and $[1/0,0]$ quadratic approximant are quite poor approximation, but its $[1/0,1]$ version already model perfectly the RMP energy function by predicting a single pair of EPs at $\lambda_\text{EP} = \pm i 4t/U$. This is expected knowing the form of the RMP energy [see Eq.~\eqref{eq:E0MP}] which perfectly suits the purpose of quadratic approximants.