Most textbooks on Kohn-Sham density functional theory will assert that it is exact assuming that one has the 'appropriate' exchange-correlation functional. To my mind, this is completely astounding and would imply that irrespective of the strength of correlations there is always a single particle picture. Will this always be true in the limit of very strong correlations e.g. at quantum critical points? Aside from this, are there physical situations in which the exchange-correlation functional is sufficiently ill-behaved so as for the Hohenberg-Kohn theorems to not apply?
EDIT: I have realized that my question is rather vague. The question that I meant to ask is whether the exact exchange-correlation functional can exist for a strongly correlated system. My justification for believing this might be correct is that I would expect a perturbative expansion of the self-energy $\Sigma (\mathbf k)$ to diverge rapidly in a highly correlated system.