forgotten references
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\begin{thebibliography}{141}%
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\begin{thebibliography}{131}%
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\makeatletter
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\providecommand \@ifxundefined [1]{%
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@ -1060,25 +1060,6 @@
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{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo
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{pages} {134112} (\bibinfo {year} {2019}{\natexlab{d}})}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Sergeev}\ \emph {et~al.}(2005)\citenamefont
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{Sergeev}, \citenamefont {Goodson}, \citenamefont {Wheeler},\ and\
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\citenamefont {Allen}}]{Sergeev_2005}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~V.}\ \bibnamefont
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{Sergeev}}, \bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}}, \bibinfo {author} {\bibfnamefont {S.~E.}\ \bibnamefont
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{Wheeler}}, \ and\ \bibinfo {author} {\bibfnamefont {W.~D.}\ \bibnamefont
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{Allen}},\ }\href {\doibase 10.1063/1.1991854} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {123}},\
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\bibinfo {pages} {064105} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Sergeev}\ and\ \citenamefont
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{Goodson}(2006)}]{Sergeev_2006}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~V.}\ \bibnamefont
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{Sergeev}}\ and\ \bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}},\ }\href {\doibase 10.1063/1.2173989} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {124}},\
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\bibinfo {pages} {094111} (\bibinfo {year} {2006})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Stillinger}(2000)}]{Stillinger_2000}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {F.~H.}\ \bibnamefont
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@ -1092,6 +1073,17 @@
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{journal} {\bibinfo {journal} {Rev. Mod. Phys.}\ }\textbf {\bibinfo {volume}
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{43}},\ \bibinfo {pages} {479} (\bibinfo {year} {1971})}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Sergeev}\ \emph {et~al.}(2005)\citenamefont
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{Sergeev}, \citenamefont {Goodson}, \citenamefont {Wheeler},\ and\
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\citenamefont {Allen}}]{Sergeev_2005}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~V.}\ \bibnamefont
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{Sergeev}}, \bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}}, \bibinfo {author} {\bibfnamefont {S.~E.}\ \bibnamefont
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{Wheeler}}, \ and\ \bibinfo {author} {\bibfnamefont {W.~D.}\ \bibnamefont
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{Allen}},\ }\href {\doibase 10.1063/1.1991854} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {123}},\
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\bibinfo {pages} {064105} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Goodson}\ and\ \citenamefont
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{Sergeev}(2004)}]{Goodson_2004}%
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\BibitemOpen
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@ -1101,6 +1093,28 @@
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{\bibinfo {booktitle} {Adv. Quantum Chem.}}},\ Vol.~\bibinfo {volume} {47}\
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(\bibinfo {publisher} {Academic Press},\ \bibinfo {year} {2004})\ pp.\
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\bibinfo {pages} {193--208}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Goodson}(2000{\natexlab{a}})}]{Goodson_2000a}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}},\ }\href {\doibase 10.1063/1.481044} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {112}},\
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\bibinfo {pages} {4901} (\bibinfo {year} {2000}{\natexlab{a}})}\BibitemShut
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\bibitem [{\citenamefont {Goodson}(2000{\natexlab{b}})}]{Goodson_2000b}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}},\ }\href {\doibase 10.1063/1.1318740} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {113}},\
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\bibinfo {pages} {6461} (\bibinfo {year} {2000}{\natexlab{b}})}\BibitemShut
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\bibitem [{\citenamefont {Sergeev}\ and\ \citenamefont
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{Goodson}(2006)}]{Sergeev_2006}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~V.}\ \bibnamefont
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{Sergeev}}\ and\ \bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}},\ }\href {\doibase 10.1063/1.2173989} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {124}},\
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\bibinfo {pages} {094111} (\bibinfo {year} {2006})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Heiss}\ and\ \citenamefont
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{M{\"u}ller}(2002)}]{Heiss_2002}%
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\BibitemOpen
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@ -1165,109 +1179,6 @@
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}\href {\doibase 10.1103/PhysRevC.71.011304} {\bibfield {journal} {\bibinfo
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{journal} {Phys. Rev. C}\ }\textbf {\bibinfo {volume} {71}},\ \bibinfo
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{pages} {011304} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Caprio}\ \emph {et~al.}(2008)\citenamefont {Caprio},
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\citenamefont {Cejnar},\ and\ \citenamefont {Iachello}}]{Caprio_2008}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.~A.}\ \bibnamefont
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{Caprio}}, \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Cejnar}}, \
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and\ \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Iachello}},\ }\href
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{\doibase 10.1016/j.aop.2007.06.011} {\bibfield {journal} {\bibinfo
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{journal} {Ann. Phys. (N. Y.)}\ }\textbf {\bibinfo {volume} {323}},\ \bibinfo
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{pages} {1106} (\bibinfo {year} {2008})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ and\ \citenamefont
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{Jolie}(2009)}]{Cejnar_2009}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}}\ and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Jolie}},\
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}\href {\doibase 10.1016/j.ppnp.2008.08.001} {\bibfield {journal} {\bibinfo
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{journal} {Prog. Part. Nucl. Phys.}\ }\textbf {\bibinfo {volume} {62}},\
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\bibinfo {pages} {210} (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Sachdev}(2011)}]{Sachdev_2011}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
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{Sachdev}},\ }\href {\doibase 10.1017/CBO9780511973765} {\emph {\bibinfo
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{title} {{Quantum Phase Transitions}}}}\ (\bibinfo {publisher} {Cambridge
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University Press},\ \bibinfo {year} {2011})\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ \emph {et~al.}(2015)\citenamefont {Cejnar},
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\citenamefont {Str{\'a}nsk{\'y}},\ and\ \citenamefont {Kloc}}]{Cejnar_2015}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}}, \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Str{\'a}nsk{\'y}}}, \ and\ \bibinfo {author} {\bibfnamefont
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{M.}~\bibnamefont {Kloc}},\ }\href {\doibase 10.1088/0031-8949/90/11/114015}
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{\bibfield {journal} {\bibinfo {journal} {Phys. Scr.}\ }\textbf {\bibinfo
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{volume} {90}},\ \bibinfo {pages} {114015} (\bibinfo {year}
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{2015})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ and\ \citenamefont
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{Str{\'a}nsk{\'y}}(2016)}]{Cejnar_2016}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}}\ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Str{\'a}nsk{\'y}}},\ }\href {\doibase 10.1088/0031-8949/91/8/083006}
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{\bibfield {journal} {\bibinfo {journal} {Phys. Scr.}\ }\textbf {\bibinfo
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{volume} {91}},\ \bibinfo {pages} {083006} (\bibinfo {year}
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{2016})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Macek}\ \emph {et~al.}(2019)\citenamefont {Macek},
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\citenamefont {Str{\'a}nsk{\'y}}, \citenamefont {Leviatan},\ and\
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\citenamefont {Cejnar}}]{Macek_2019}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
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{Macek}}, \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Str{\'a}nsk{\'y}}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
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{Leviatan}}, \ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}},\ }\href {\doibase 10.1103/PhysRevC.99.064323} {\bibfield
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{journal} {\bibinfo {journal} {Phys. Rev. C}\ }\textbf {\bibinfo {volume}
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{99}},\ \bibinfo {pages} {064323} (\bibinfo {year} {2019})}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ \emph {et~al.}(2020)\citenamefont {Cejnar},
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\citenamefont {Str{\'a}nsk{\'y}}, \citenamefont {Macek},\ and\ \citenamefont
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{Kloc}}]{Cejnar_2020}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}}, \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Str{\'a}nsk{\'y}}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
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{Macek}}, \ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Kloc}},\
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}\href@noop {} {\enquote {\bibinfo {title} {Excited-state quantum phase
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transitions},}\ } (\bibinfo {year} {2020}),\ \Eprint
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{http://arxiv.org/abs/2011.01662} {arXiv:2011.01662 [quant-ph]} \BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Str{\'a}nsk{\'y}}\ \emph {et~al.}(2018)\citenamefont
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{Str{\'a}nsk{\'y}}, \citenamefont {Dvo{\v r}{\'a}k},\ and\ \citenamefont
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{Cejnar}}]{Stransky_2018}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Str{\'a}nsk{\'y}}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
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{Dvo{\v r}{\'a}k}}, \ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}},\ }\href {\doibase 10.1103/PhysRevE.97.012112} {\bibfield
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{journal} {\bibinfo {journal} {Phys. Rev. E}\ }\textbf {\bibinfo {volume}
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{97}},\ \bibinfo {pages} {012112} (\bibinfo {year} {2018})}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Lipkin}\ \emph {et~al.}(1965)\citenamefont {Lipkin},
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\citenamefont {Meshkov},\ and\ \citenamefont {Glick}}]{Lipkin_1965}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {H.~J.}\ \bibnamefont
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{Lipkin}}, \bibinfo {author} {\bibfnamefont {N.}~\bibnamefont {Meshkov}}, \
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and\ \bibinfo {author} {\bibfnamefont {A.~J.}\ \bibnamefont {Glick}},\ }\href
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{\doibase 10.1016/0029-5582(65)90862-X} {\bibfield {journal} {\bibinfo
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{journal} {Nucl. Phys.}\ }\textbf {\bibinfo {volume} {62}},\ \bibinfo {pages}
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{188} (\bibinfo {year} {1965})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ and\ \citenamefont
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{Jolie}(2000)}]{Cejnar_2000}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}}\ and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Jolie}},\
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}\href {\doibase 10.1103/PhysRevE.61.6237} {\bibfield {journal} {\bibinfo
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{journal} {Phys. Rev. E}\ }\textbf {\bibinfo {volume} {61}},\ \bibinfo
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{pages} {6237} (\bibinfo {year} {2000})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ \emph {et~al.}(2003)\citenamefont {Cejnar},
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\citenamefont {Heinze},\ and\ \citenamefont {Jolie}}]{Cejnar_2003}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{Cejnar}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Heinze}}, \
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and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Jolie}},\ }\href
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{\doibase 10.1103/PhysRevC.68.034326} {\bibfield {journal} {\bibinfo
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{journal} {Phys. Rev. C}\ }\textbf {\bibinfo {volume} {68}},\ \bibinfo
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{pages} {034326} (\bibinfo {year} {2003})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Cejnar}\ and\ \citenamefont
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{Iachello}(2007)}]{Cejnar_2007a}%
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\BibitemOpen
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@ -1341,12 +1252,6 @@
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{\bibinfo {journal} {J. Phys. C.: Solid State Phys.}\ }\textbf {\bibinfo
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{volume} {18}},\ \bibinfo {pages} {3297} (\bibinfo {year}
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{1985})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Goodson}(2000)}]{Goodson_2000}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~Z.}\ \bibnamefont
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{Goodson}},\ }\href {\doibase 10.1063/1.481044} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {112}},\
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\bibinfo {pages} {4901} (\bibinfo {year} {2000})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Surj{\'a}n}\ and\ \citenamefont
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{Szabados}(2000)}]{Surjan_2000}%
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\BibitemOpen
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@ -1,13 +1,39 @@
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-11-25 22:26:55 +0100
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%% Created for Pierre-Francois Loos at 2020-11-27 20:55:11 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@article{Kais_2006,
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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.},
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author = {Sabre Kais and Craig Wenger and Qi Wei},
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date-added = {2020-11-27 20:54:34 +0100},
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date-modified = {2020-11-27 20:55:08 +0100},
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doi = {https://doi.org/10.1016/j.cplett.2006.03.035},
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journal = {Chem. Phys. Lett.},
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pages = {45 - 49},
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title = {Quantum criticality at the infinite complete basis set limit: A thermodynamic analog of the Yang and Lee theorem},
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volume = {423},
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year = {2006},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261406003897},
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Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2006.03.035}}
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@article{Goodson_2000b,
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author = {Goodson,David Z.},
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date-added = {2020-11-27 20:42:57 +0100},
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date-modified = {2020-11-27 20:43:12 +0100},
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doi = {10.1063/1.1318740},
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journal = {J. Chem. Phys.},
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pages = {6461-6464},
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title = {A summation procedure that improves the accuracy of the fourth-order Mo/ller--Plesset perturbation theory},
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volume = {113},
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year = {2000},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.1318740}}
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@article{Pavlyukh_2017,
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author = {Y. Pavlyukh},
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date-added = {2020-11-25 22:26:26 +0100},
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@ -33,10 +59,10 @@
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.99.075149},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.99.075149}}
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@article{Goodson_2000,
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@article{Goodson_2000a,
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author = {Goodson,David Z.},
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date-added = {2020-11-25 10:05:02 +0100},
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date-modified = {2020-11-25 10:05:17 +0100},
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date-modified = {2020-11-27 20:42:22 +0100},
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doi = {10.1063/1.481044},
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journal = {J. Chem. Phys.},
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pages = {4901-4909},
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@ -1179,7 +1179,7 @@ To further develop the link between the critical point and types of MP convergen
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the relationship with the location of the dominant singularity that controls the radius of convergence.\cite{Goodson_2004}.
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They demonstrated that the dominant singularity in class A corresponds to a dominant EP with a positive real component,
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with the magnitude of the imaginary component controlling the oscillations in the signs of the MP
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term.\cite{Goodson_2000a,Goodson200b}
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term.\cite{Goodson_2000a,Goodson_2000b}
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In contrast, class B systems correspond to a dominant singularity on the negative real $\lambda$ axis representing
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the MP critical point.
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The divergence of class B systems, which contain closely spaced electrons (\eg, \ce{F-}), can then be understood as the
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@ -1383,7 +1383,7 @@ and substituting $E(\lambda$) by its $n$th-order expansion and the polynomials b
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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 $P^2(\lambda) - 4 Q(\lambda) R(\lambda)$.
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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.
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Note that, by construction, a quadratic approximant has only two branches which hampers the faithful description of more complicated singularity structures.
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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}
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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}
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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 $\lambda_\text{EP} = \pm i 4t/U$.
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This is expected knowing the form of the RMP energy [see Eq.~\eqref{eq:E0MP}] which perfectly suits the purpose of quadratic approximants.
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