Electronic excited states in extreme limits via ensemble density functionals

Density functional theory (DFT) has greatly expanded our ability to affordably compute and understand electronic ground states, by replacing intractable {\em ab initio} calculations by models based on paradigmatic physics from high- and low-density limits. But, a comparable treatment of excited states lags behind. Here, we solve this outstanding problem by employing a generalization of density functional theory to ensemble states (EDFT). We thus address important paradigmatic cases of all electronic systems in strongly (low-density) and weakly (high-density) correlated regimes. We show that the high-density limit connects to recent, exactly-solvable EDFT results. The low-density limit reveals an unnoticed and most unexpected result -- density functionals for strictly correlated {\em ground} states can be reused {\em directly} for excited states. Non-trivial dependence on excitation structure only shows up at third leading order. Overall, our results provide foundations for effective models of excited states that interpolate between exact low- and high-density limits, which we illustrate on the cases of singlet-singlet excitations in H$_2$ and a ring of quantum wells.