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small energies. Here $\Sigma_{HF} $ is the self energy computed in the Hartree Fock approximation. At infinite frequency,  $\Sigma $ is given by the Hartree Fock graph evaluated with the exact Greens function, hence the Hartree Fock approximation is not exact even at infinite frequency, but it is a good starting point for the treatment of atoms and molecules.   Solid state physicists adopt a very different definition of strong correlations. Here, a good reference system is the Kohn-Sham Greens function evaluated in some implementation of the density functional theory such as the LDA. Hence, for condensed matter scientists, by definition, a strongly correlated material is one where $\Sigma - V_{KS} V_\text{xc}  $ is large at low frequencies. Strongly correlated materials, are those for which this is not the case, a famous example are materials such as La2CuO4 which are predicted to be metals in LDA but which are experimentally antiferromagnetic Mott insulators. In quantum chemistry~\cite{Mori_S_nchez_2008}, there is a classification of the errors introduced by the use of approximate density functionals, as being of two types, static correlation and dynamic correlation\cite{Yang_2012}. Similar ideas, also appear in the solid state context, but the nomenclature is exchanged. A \emph{static} self energy (i.e. a self energy which varies weakly with frequency at low energies) corresponds to the concept of dynamical correlations.