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@ -19,7 +19,7 @@ In particular, we focus on its mathematical roots and connections with physical
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We begin by presenting the fundamental concepts behind non-Hermitian extensions of quantum chemistry into the complex plane, including the Hartree--Fock approximation and
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Rayleigh--Schr\"odinger perturbation theory.
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We then provide a comprehensive review of the various research that has been performed around the physics of complex singularities in perturbation theory, with a particular focus on M{\o}ller--Plesset theory.
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Finally, several resummation techniques are discussedthat can improve energy estimates for both convergent and divergent series, including Pad\'e and quadratic approximants.
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Finally, several resummation techniques are discussed that can improve energy estimates for both convergent and divergent series, including Pad\'e and quadratic approximants.
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Throughout this review, we present illustrative and pedagogical examples based on the ubiquitous Hubbard dimer at half-filling, reinforcing the amazing versatility of this powerful simplistic model.
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Due to the genuine interdisciplinary nature of the present article and its pedagogical aspect, we believe that it will be of interest to a wide audience within the physics and chemistry communities.
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@ -168,7 +168,7 @@ Each of these points is pedagogically illustrated using the Hubbard dimer at hal
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% SPIKE THE READER
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Perturbation theory isn't usually considered in the complex plane.
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Normally it is applied using real numbers as one of very few availabe tools for
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describing realistic quantum systems where exact solutions of the Schr\"odinger equation are impossible.\cite{Dirac_1929}
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describing realistic quantum systems where exact solutions of the Schr\"odinger equation are impossible \titou{to find?}.\cite{Dirac_1929}
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In particular, time-independent Rayleigh--Schr\"odinger perturbation theory\cite{RayleighBook,Schrodinger_1926}
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has emerged as an instrument of choice among the vast array of methods developed for this purpose.%
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\cite{SzaboBook,JensenBook,CramerBook,HelgakerBook,ParrBook,FetterBook,ReiningBook}
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