Title: A `simple metal' description of liquid carbon, its warm-dense matter states, and the identification of liquid-liquid phase transitions

Abstract: Liquid carbon is a complex fluid whose theory is claimed to require explicit covalent interactions and many-center potentials. Thus very expensive $N$-atom quantum simulations for $N\sim 100-500$ using density-functional theory (DFT), and molecular-dynamics (MD) are usually deployed. They show intriguing structure factors with a split first peak and features not found in simple metallic liquids. We show that a {\it simple-metal} model using only one-body electron densities, one-body ion densities, and appropriate exchange-correlation functionals implemented in the one-atom DFT approach of the neutral pseudo-atom (NPA) model, quantitatively and inexpensively recovers the results of $N$-atom DFT simulations. We show that structural changes are dominated by strong electron-ion interactions at the Fermi energy. Evidence is presented for three liquid-liquid phase transitions in the 3 to 4 g/cm$^3$ range using NPA calculations supported by DFT-MD simulations.