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intro

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Pierre-Francois Loos 2020-12-04 09:25:33 +01:00
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@ -152,7 +152,7 @@ We observe that the physics of a quantum system is intimately connected to the p
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, 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.
We also discuss several resummation techniques (such as Pad\'e and quadratic approximants) able to improve the overall accuracy of the M{\o}ller--Plesset perturbative series in both convergent and divergent cases.
Each of these points is further illustrated with the ubiquitous Hubbard dimer at half filling which proves to be a versatile model system in order to understand the subtle concepts of the analytic continuation of perturbation theory in the complex plane.
Each of these points is further illustrated with the ubiquitous Hubbard dimer at half filling which proves to be a versatile model system in order to understand the subtle concepts of the analytic continuation of perturbation theory into the complex plane.
\end{abstract}
\maketitle
@ -255,11 +255,11 @@ be harnessed to significantly improve estimates of the exact energy using only t
in the MP series.
The present review is organised as follows.
In Sec.~\ref{sec:EPs}, we introduce key concepts, such as Rayleigh-Schr\"odinger perturbation theory and the mean-field HF approximation, and discuss their extension to the complex plane.
In Sec.~\ref{sec:EPs}, we introduce key concepts, such as Rayleigh-Schr\"odinger perturbation theory and the mean-field HF approximation, and discuss their analytic continuation into the complex plane.
Section \ref{sec:MP} deals with MP perturbation theory and we report an exhaustive historical overview of the various research activities that have been performed on the physics of singularities.
We discuss several resummation techniques (such as Pad\'e and quadratic approximants) in Sec.~\ref{sec:Resummation}.
Finally, we draw our conclusions in Sec.~\ref{sec:ccl}.
For most of the concepts presented in this review, we report concrete illustrative and pedagogical examples based on the ubiquitous Hubbard dimer, showing the amazing versatility of this simple yet powerful model system.
For most of the concepts presented in this review, we report illustrative and pedagogical examples based on the ubiquitous Hubbard dimer, showing the amazing versatility of this simple yet powerful model system.
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\section{Exceptional Points in Electronic Structure}