218 lines
18 KiB
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218 lines
18 KiB
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\@writefile{toc}{\contentsline {subsection}{\numberline {E}Requirements for the approximated functionals in the strong correlation regime}{5}{section*.11}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Condition for the functional $\mathaccentV {bar}916{E}_{\text {X}}^\mathcal {B}[{n},\xi ,s,n^{(2)},\mu _{\Psi ^{\mathcal {B}}}]$ to obtain $S_z$ invariance}{5}{section*.13}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Conditions on $\Psi ^{\mathcal {B}}$ for the extensivity}{5}{section*.14}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {F}Different types of approximations for the functional}{5}{section*.15}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Definition of the protocol to design functionals}{5}{section*.16}}
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\citation{GorSav-PRA-06}
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\citation{FerGinTou-JCP-18,GinSceTouLoo-JCP-19}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Definition of a hierarchy of functionals}{6}{section*.17}}
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{6}{section*.18}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A}Numerical tests of extensivity}{6}{section*.19}}
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\bibcite{Thom-PRL-10}{{1}{2010}{{Thom}}{{}}}
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\bibcite{ScoTho-JCP-17}{{2}{2017}{{Scott\ and\ Thom}}{{}}}
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\bibcite{SpeNeuVigFraTho-JCP-18}{{3}{2018}{{Spencer\ \emph {et~al.}}}{{Spencer, Neufeld, Vigor, Franklin,\ and\ Thom}}}
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\bibcite{DeuEmiYumShePie-JCP-19}{{6}{2019}{{Deustua\ \emph {et~al.}}}{{Deustua, Yuwono, Shen,\ and\ Piecuch}}}
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\bibcite{QiuHenZhaScu-JCP-17}{{7}{2017}{{Qiu\ \emph {et~al.}}}{{Qiu, Henderson, Zhao,\ and\ Scuseria}}}
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\bibcite{QiuHenZhaScu-JCP-18}{{8}{2018}{{Qiu\ \emph {et~al.}}}{{Qiu, Henderson, Zhao,\ and\ Scuseria}}}
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\bibcite{GomHenScu-JCP-19}{{9}{2019}{{Gomez, Henderson,\ and\ Scuseria}}{{}}}
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\bibcite{WerKno-JCP-88}{{10}{1988}{{Werner\ and\ Knowles}}{{}}}
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\bibcite{KnoWer-CPL-88}{{11}{1988}{{Knowles\ and\ Werner}}{{}}}
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\bibcite{BenErn-PhysRev-1969}{{12}{1969}{{Bender\ and\ Davidson}}{{}}}
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\bibcite{WhiHac-JCP-1969}{{13}{1969}{{Whitten\ and\ Hackmeyer}}{{}}}
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\bibcite{HurMalRan-1973}{{14}{1973}{{Huron, Malrieu,\ and\ Rancurel}}{{}}}
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\bibcite{EvaDauMal-ChemPhys-83}{{15}{1983}{{Evangelisti, Daudey,\ and\ Malrieu}}{{}}}
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\bibcite{Cim-JCC-1987}{{17}{1987}{{Cimiraglia\ and\ Persico}}{{}}}
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\bibcite{IllRubRic-JCP-88}{{18}{1988}{{Illas, Rubio,\ and\ Ricart}}{{}}}
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\bibcite{PovRubIll-TCA-92}{{19}{1992}{{Povill, Rubio,\ and\ Illas}}{{}}}
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\bibcite{AbrSheDav-CPL-05}{{21}{2005}{{Abrams\ and\ Sherrill}}{{}}}
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\bibcite{MusEngels-JCC-06}{{22}{2006}{{Musch\ and\ Engels}}{{}}}
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\bibcite{BytRue-CP-09}{{23}{2009}{{Bytautas\ and\ Ruedenberg}}{{}}}
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\bibcite{GinSceCaf-CJC-13}{{24}{2013}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
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\bibcite{CafGinScemRam-JCTC-14}{{25}{2014}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Giner, Scemama,\ and\ Ram{\'\i }rez-Sol{\'\i }s}}}
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\bibcite{GinSceCaf-JCP-15}{{26}{2015}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
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\bibcite{CafAplGinScem-arxiv-16}{{27}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
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\bibcite{CafAplGinSce-JCP-16}{{28}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
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\bibcite{SchEva-JCP-16}{{29}{2016}{{Schriber\ and\ Evangelista}}{{}}}
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\bibcite{Zim-JCP-17}{{36}{2017}{{Zimmerman}}{{}}}
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\bibcite{LiOttHolShaUmr-JCP-2018}{{37}{2018}{{Li\ \emph {et~al.}}}{{Li, Otten, Holmes, Sharma,\ and\ Umrigar}}}
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\bibcite{ChiHolOttUmrShaZim-JPCA-18}{{38}{2018}{{Chien\ \emph {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
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\bibcite{SceBenJacCafLoo-JCP-18}{{39}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
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\bibcite{LooSceBloGarCafJac-JCTC-18}{{40}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
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\bibcite{SceGarCafLoo-JCTC-18}{{42}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Garniron, Caffarel,\ and\ Loos}}}
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\bibcite{GarGinMalSce-JCP-16}{{43}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Giner, Malrieu,\ and\ Scemama}}}
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\bibcite{LooBogSceCafJac-JCTC-19}{{44}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
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\bibcite{Kut-TCA-85}{{46}{1985}{{Kutzelnigg}}{{}}}
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\bibcite{KutKlo-JCP-91}{{47}{1991}{{Kutzelnigg\ and\ Klopper}}{{}}}
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\bibcite{MaWer-WIREs-18}{{56}{2018}{{Ma\ and\ Werner}}{{}}}
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\bibcite{TewKloNeiHat-PCCP-07}{{57}{2007}{{Tew\ \emph {et~al.}}}{{Tew, Klopper, Neiss,\ and\ Hattig}}}
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\bibcite{TouZhuSavJanAng-JCP-11}{{64}{2011}{{Toulouse\ \emph {et~al.}}}{{Toulouse, Zhu, Savin, Jansen,\ and\ \'Angy\'an}}}
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