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catch -> captures

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Pierre-Francois Loos 2022-10-19 00:34:33 +02:00
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CCvsMBPT.tex
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@ -168,7 +168,7 @@ In particular, it may provide a path for the computation of ground- and excited-
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The random-phase approximation (RPA), introduced by Bohm and Pines \cite{Bohm_1951,Pines_1952,Bohm_1953} in the context of the uniform electron gas, \cite{Loos_2016} is a quasibosonic approximation where one treats fermion products as bosons. The random-phase approximation (RPA), introduced by Bohm and Pines \cite{Bohm_1951,Pines_1952,Bohm_1953} in the context of the uniform electron gas, \cite{Loos_2016} is a quasibosonic approximation where one treats fermion products as bosons.
In the particle-hole (ph) channel, which is quite popular in the electronic structure community, \cite{Ren_2012,Chen_2017} particle-hole fermionic excitations and deexcitations are assumed to be bosons. In the particle-hole (ph) channel, which is quite popular in the electronic structure community, \cite{Ren_2012,Chen_2017} particle-hole fermionic excitations and deexcitations are assumed to be bosons.
Because ph-RPA takes into account dynamical screening by summing up to infinity the (time-independent) ring diagrams, it is adequate in the high-density (or weakly correlated) regime and catch effectively long-range correlation effects (such as dispersion). \cite{Gell-Mann_1957,Nozieres_1958} Because ph-RPA takes into account dynamical screening by summing up to infinity the (time-independent) ring diagrams, it is adequate in the high-density (or weakly correlated) regime and captures effectively long-range correlation effects (such as dispersion). \cite{Gell-Mann_1957,Nozieres_1958}
Another important feature of ph-RPA compared to finite-order perturbation theory is that it does not exhibit divergences for small-gap or metallic systems. \cite{Gell-Mann_1957} Another important feature of ph-RPA compared to finite-order perturbation theory is that it does not exhibit divergences for small-gap or metallic systems. \cite{Gell-Mann_1957}
Roughly speaking, the Bethe-Salpeter equation (BSE) formalism \cite{Salpeter_1951,Strinati_1988,Blase_2018,Blase_2020} of many-body perturbation theory \cite{Martin_2016} can be seen as a cheap and efficient way of introducing correlation in order to go \textit{beyond} RPA physics. Roughly speaking, the Bethe-Salpeter equation (BSE) formalism \cite{Salpeter_1951,Strinati_1988,Blase_2018,Blase_2020} of many-body perturbation theory \cite{Martin_2016} can be seen as a cheap and efficient way of introducing correlation in order to go \textit{beyond} RPA physics.