corrected Moller-Plesset em-dash throughout

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Hugh Burton 2020-11-24 14:18:22 +00:00
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In this review, we explore the extension of quantum chemistry in the complex plane and its link with perturbation theory.
We observe that the physics of a quantum system is intimately connected to the position of energy singularities in the complex plane, known as exceptionnal points.
After a presentation of the fundamental notions of quantum chemistry in the complex plane, such as the mean-field Hartree-Fock approximation and Rayleigh-Schr\"odinger perturbation theory, and their illustration with the ubiquitous (symmetric) Hubbard dimer at half filling, we provide a historical overview of the various research activities that have been performed on the physics of singularities.
In particular, we highlight the seminal work of several research groups on the convergence behaviour of perturbative series obtained within M{\o}ller-Plesset perturbation theory and its apparent link with quantum phase transitions.
In particular, we highlight the seminal work of several research groups on the convergence behaviour of perturbative series obtained within M{\o}ller--Plesset perturbation theory and its apparent link with quantum phase transitions.
\end{abstract}
\maketitle
@ -629,7 +629,7 @@ role of \textit{quasi}-EPs in determining the behaviour of the HF approximation.
%Through the introduction of non-Hermiticity, we have provided a more general framework in which the complex and diverse characteristics of multiple solutions can be explored and understood.}
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\section{M{\o}ller-Plesset Perturbation Theory in the Complex Plane}
\section{M{\o}ller--Plesset Perturbation Theory in the Complex Plane}
\label{sec:MP}
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@ -706,7 +706,7 @@ their relative strengths and weaknesses for various situations, we will restrict
to the convergence properties of the MP expansion.
%=====================================================%
\subsection{Early Investigations into M{\o}ller-Plesset Convergence} % in Molecular Systems}
\subsection{Early Investigations into M{\o}ller--Plesset Convergence} % in Molecular Systems}
%=====================================================%
% GENERAL DESIRE FOR WELL-BEHAVED CONVERGENCE AND LOW-ORDER TERMS