Excited states of the uniform electron gas

The uniform electron gas (UEG) is a cornerstone of density-functional theory (DFT) and the foundation of the local-density approximation, one of the most successful approximations in DFT. In this work, we extend the concept of UEG by introducing excited-state UEGs, systems characterized by a gap at the Fermi surface created by the excitation of electrons near the Fermi level. We report closed-form expressions of the reduced kinetic and exchange energies of these excited-state UEGs as functions of the density and the gap. In addition, we derive the leading term of the correlation energy in the high-density limit. By incorporating an additional variable representing the degree of excitation into the UEG paradigm, the present work introduces a new framework for constructing local and semi-local state-specific functionals for excited states.