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strongly correlated material is one where $\Sigma - V_{KS} $ is large at low frequencies. Strongly correlated materials, are those for which this is not the case, a famous example are materials such as LaCuO4 which are predicted to be metals in LDA but which are experimentally antiferromagnetic Mott insulators.   In quantum chemistry   Aron J Cohen, Paula Mori-Sánchez, Weitao Yang (2008) Science 321,792-794 \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 {\it static } self energy   (i.e. a self energy which varies weakly with frequency at low energies) corresponds to the concept of dynamical correlations.