Hydrogen plasmas beyond density-functional theory: Dynamic correlations and the onset of localization

We examine the onset of bound (i.e., localized) states in a high-temperature plasma consisting of electrons and ions. The onset of localization or ionization is related to the Mott and Anderson transitions of condensed-matter physics and to the breakdown of the Saha equation. We consider several models and develop a physically reasonable model of a plasma based on density-functional theory (DFT) where the mean ionic charge $\bar{Z}$ interpolates from the fully ionized limit to the atomic limit. This DFT model provides structure factors and Kohn-Sham eigenstates which are then used to calculate the self-energy of the one-electron Green function, thus transcending the local-density approximation and the well-known limitations of DFT, especially with regard to the excitation spectrum. The self-energy contains contributions from electron-electron and electron-ion density fluctuation effects, screening effects, and the renormalization of the propagators. The calculation yields shifted energy levels, widths, and level populations. The level widths are shown to be closely related to the electrical conductivity of Ziman-type formulations. The one-particle formalism used makes contact with the multiple-scattering theories of disordered materials, liquid metals, etc., and is a necessary first step to a future calculation of two-particle propagators and related properties.