Understanding the properties of matter under extreme densities, temperatures and pressures has emerged as a highly active frontier at the interface of plasma and solid state physics, quantum chemistry and material science. In nature, such warm dense matter (WDM) abounds in a number of astrophysical objects including giant planet interiors, brown and white dwarf, and the outer layer of neutron stars. On Earth, WDM plays an increasingly important role for material science, synthesis and discovery. A particularly exciting application is given by inertial confinement fusion, where, during the initial stage of the compression path, both the fusion fuel and the surrounding ablator material have to traverse the WDM regime in a controlled way to reach ignition.
From a theoretical perspective, the rigorous description of WDM constitutes a most formidable challenge as it must holistically treat the complex interplay of effects such as Coulomb coupling, quantum degeneracy, strong thermal excitation, and partial ionization. This is difficult even for state-of-the-art density functional theory simulations, which require external input in the form of the electronic exchange-correlation (XC) functional. While the accuracy of various XC-functional approximations is reasonably well understood at ambient conditions, the development of explicitly thermal XC-functionals that consistently take into account temperature effects remains in its infancy. In addition, novel developments are hampered by the almost complete absence of reliable benchmark data.
Within PREXTREME, we aim to fundamentally change this unsatisfactory situation by developing cutting-edge path integral Monte Carlo (PIMC) simulations. The key strength of the PIMC method is that it is a) approximation-free and b) does not require any empirical external input. The main limitation is the notorious fermion sign problem---an exponential computational bottleneck that poses great practical limitations within physics, quantum chemistry, and increasingly also material science and computational biology. PREXTREME will first push the boundaries of existing PIMC methodologies to obtain the first exact simulation results for a number of light elements over substantial parts of the relevant WDM parameter space; in addition to being very interesting in their own right, these simulation results will also constitute invaluable benchmark data for commonly used theoretical models and approximations. Finally, we aim to develop a controlled, systematic and fundamental solution to the fermion sign problem by combining PIMC with modern machine-learning techniques. The resulting sign-problem free PIMC implementation will be made openly available and has the potential to be a true game changer for the simulation of quantum many-body systems in a plethora of research fields.
