Comparing first-principles methods for computing electrical conductivity in warm dense matter

DC electrical conductivity is a critical input for hydrodynamic simulations of high-energy-density systems. Large uncertainties in the warm dense regime require accurate theoretical methods to constrain more efficient models capable of tabulating properties over a wide range of conditions. Density functional theory with the Kubo-Greenwood formula (DFT-KG) and real-time time-dependent density functional theory (TDDFT) give two related but independent approaches for computing dynamic conductivities from first principles. These two methods involve subtly different underlying assumptions, exhibit different scaling with respect to system size, and present distinct numerical challenges. We perform a detailed comparison of DFT-KG and TDDFT predictions for the electrical conductivity of warm dense aluminum, hydrogen, and beryllium, paying special attention to computational properties and convergence behavior. This work will help identify the most effective first-principles framework for obtaining precise conductivity data in various thermodynamic and frequency regimes.