Abstract:

Warm dense matter is a highly energetic phase, intermediate to solids, liquids, and plasma. It is found in such diverse environments as the centers of giant planets, within small stars, and during the ignition of inertial confinement fusion capsules, and it is so complicated to model that some call it, "the malfunction junction." Thermal density functional theory is common in simulations of these high-temperature, high-density materials, despite the scarcity of explicitly temperature-dependent approximations and disagreement over the impact of these missing thermal effects on calculated properties.  Adiabatic connection approaches have long been used in ground-state density functional theory for analyzing exact and approximate density functional theory, and it has more recently been applied to both thermal and ensemble versions of the theory. In this talk, I'll introduce the adiabatic connection and what changes for this tool when at the high temperatures and densities common to warm dense matter. I will then discuss how we use the adiabatic connection to explore limiting behavior of the exchange-correlation free energy and to develop new ways to approximate temperature dependence. Insights from both ensemble density functional theory and the electronic strong-interaction limit can be applied to thermal ensembles, creating new approximation schemes and serving to connect these branches of formal theory with thermal density functional theory and its applications. Numerical demonstrations using the finite-temperature asymmetric Hubbard dimer and the uniform electron gas will be used to examine the advantages and disadvantages of the two approaches, and the new generalized thermal adiabatic connection approach will be described.