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 \begin{abstract}
-We explore the extension of quantum chemistry in the complex plane and its link with perturbation theory.
+We explore the non-Hermitian 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 exceptional 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, 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 into the complex plane.
+After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including 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 links with quantum phase transitions.
+We also discuss several resummation techniques (such as Pad\'e and quadratic approximants) that can improve the overall accuracy of the M{\o}ller--Plesset perturbative series in both convergent and divergent cases.
+Each of these points is pedagogically illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane.
 \end{abstract}
 
 \maketitle