also with a recently considered variant. [@CK01] Only in the static DF theory there is a convex (density) functional. [@HK64; @KS65; @Mer65] Nevertheless, the proposed self-energy-functional approach is systematic: For any sequence of reference systems $H'$ including more and more degrees of freedom and converging to the original system $H$ there is, from the variational principle, a corresponding sequence of grand potentials which must converge to the exact $\Omega = \Omega_{\bf t} [{\bf \Sigma}({\bf t})]$ as the subspace of trial self-energies increases and eventually includes the exact self-energy ${\bf \Sigma}({\bf t})$.

Relation to the DMFT {#sec:dmft}
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Given an original model $H$, what could a suitable reference system $H'$ look like? Consider, for example, $H$ to be the Hubbard model [@hub] which is shown in Fig. 1a schematically: A filled dot represents a correlated site $i$ with on-site Hubbard interaction $U$, and a line connecting two sites $i$ and $j$ represents the nearest-neighbor hopping $t_{i,j}$. The number of sites is $L \mapsto \infty$. Fig. 1c shows a conceivable reference system $H'$. $H'$ is obtained from $H$ (Fig. 1a) by (i) adding to each correlated site $i$ a number of $n_{\rm s}-1$ uncorrelated (“bath”) sites $k=2,...,n_{\rm s}$ (open dots) which are 