Improving the Treatment of Electron-Electron Interactions in the Kubo-Greenwood Formalism

Simulations of high-energy-density experiments often rely on the resistive magnetohydrodynamic equations, which require parameters like the DC electrical conductivity for closure. State-of-the-art conductivity calculations for warm dense matter typically evaluate the Kubo-Greenwood (KG) equation using Kohn-Sham energies and wavefunctions from density functional theory (DFT). In this work, we present a first-principles approach for improving the treatment of electron-electron (e-e) interactions through many-body perturbation theory. We use the GW approximation to compute the complex electron self-energy, where the real part gives the quasiparticle (qp) energies and the imaginary part the qp lifetimes. We then modify the KG equation by replacing the DFT eigenvalues and occupations with the corresponding GW values. Further, we replace the commonly used ad hoc static broadening factor with a more rigorous dynamic form related to the qp lifetimes. Throughout, we demonstrate our approach for warm dense beryllium near solid density and at temperatures up to 7 eV. By improving the e-e interaction physics, we expect the GW approximation to improve the accuracy of the KG conductivity predictions.