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Hugh Burton 2020-11-29 09:55:14 +00:00
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Manuscript/EPAWTFT.tex
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\documentclass[aps,prb,reprint,noshowkeys,linenumbers,superscriptaddress]{revtex4-1} \documentclass[aps,prb,reprint,noshowkeys,superscriptaddress]{revtex4-1}
\usepackage{subcaption} \usepackage{subcaption}
\usepackage{bm,graphicx,tabularx,array,booktabs,dcolumn,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,siunitx,mhchem} \usepackage{bm,graphicx,tabularx,array,booktabs,dcolumn,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,siunitx,mhchem}
\usepackage[utf8]{inputenc} \usepackage[utf8]{inputenc}
@ -1226,14 +1226,14 @@ Since the MP critical point corresponds to a singularity on the real $\lambda$ a
recognised as a QPT within the perturbation theory approximation. recognised as a QPT within the perturbation theory approximation.
However, a conventional QPT can only occur in the thermodynamic limit, which here is analogous to the complete However, a conventional QPT can only occur in the thermodynamic limit, which here is analogous to the complete
basis set limit.\cite{Kais_2006} basis set limit.\cite{Kais_2006}
The MP critical point $\beta$ singularity in a finite basis must therefore be modelled by pairs of EPs The MP critical point and corresponding $\beta$ singularities in a finite basis must therefore be modelled by pairs of EPs
that tend towards the real axis, exactly as described by Sergeev \etal\cite{Sergeev_2005} that tend towards the real axis, exactly as described by Sergeev \etal\cite{Sergeev_2005}
In contrast, $\alpha$ singularities correspond to large avoided crossings that are indicative of low-lying excited In contrast, $\alpha$ singularities correspond to large avoided crossings that are indicative of low-lying excited
states which share the symmetry of the ground state,\cite{Goodson_2004} and are thus not manifestations of a QPT. states which share the symmetry of the ground state,\cite{Goodson_2004} and are thus not manifestations of a QPT.
%======================================= %=======================================
\subsection{Critical Point in the Hubbard Dimer} %\subsection{Critical Point in the Hubbard Dimer}
\label{sec:critical_point_hubbard} %\label{sec:critical_point_hubbard}
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