Frontiers of Computational Quantum Many-Body Theory

Density functional theory (DFT) simulation of warm dense matter


Linear-response time-dependent density functional theory constitutes a potentially powerful tool for the prediction of XRTS measurements. In addition to the usual XC-functional that is required for any type of DFT application, the computation of such dynamic properties needs the so-called XC-kernel as an additional input. In practice, computing an XC-kernel consistently was limited to relatively simple XC-functionals.

Recently, we have developed a novel framework that allows the direct computation of the static XC-kernel for arbitrarily complex XC-functionals. This includes nonlocal hybrid functionals, which constitute the gold standard in the field of DFT simulations.

Comparing these results with exact PIMC reference data where they are available has given new insights into the  behavior of different XC-functionals. Moreover, the presented framework constitutes the basis for a number of DFT applications such as the prediction of XRTS experiments with warm dense matter.

The key strength of the DFT method is its balance between good accuracy and a manageable computational effort. In our group, we use exact PIMC reference data to rigorously assess the accuracy of different exchange—correlation functionals in DFT for the simulation of WDM. Moreover, we use DFT to predict XRTS experiments, and to study the linear and nonlinear response properties of a variety of systems.

Over the last two decades, the DFT method has become the de-facto work horse of WDM theory as it allows one to simulate complex systems with a manageable computation cost. In practice, the accuracy of a DFT simulation decisively depends on the employed exchange—correlation (XC) functional; it cannot be obtained within DFT itself, and has to be supplied as an empirical input. While the applicability of the available zoo of approximations for the XC-functional is reasonably well understood at ambient conditions, the development of thermal XC-functionals that are specifically designed for WDM simulations has started only recently. In our group, we use our quasi-exact PIMC simulation results to unambiguously benchmark existing functionals in the WDM regime. Moreover, we explore new concepts for the construction of novel functionals that consistently take into account the effect of the temperature.

A second field of application are linear-response time-dependent DFT (LR-TDDFT) simulations of various WDM systems such as hydrogen, beryllium, and carbon to predict the outcome of X-ray Thomson scattering (XRTS) experiments. To this end, we have developed a new framework that allows us to evaluate the static XC-kernel for arbitrary XC-functionals on any level of Jacob’s ladder of functional approximations. These efforts are further aided by extensive DFT+MD (Molecular Dynamics) simulations that give us access to important structural properties of the studied system such as the Rayleigh weight, a key property for the interpretation of XRTS experiments.