Periodic Reporting for period 1 - PREXTREME (Predicting the Extreme)
Berichtszeitraum: 2023-03-01 bis 2025-08-31
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.
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.
During the first two years of the project, we have implemented a new approach to efficiently deal with the fermion sign problem into our PIMC code. It allows for the simulation of unprecedented system sizes (N=1000 electrons have been demonstrated so far) for weak to moderate levels of quantum degeneracy. A particular strength of the method is that it retains the full access to all observables, including dynamic properties encoded into various imaginary-time correlation functions. This has allowed us to present the first exact results of the density response of warm dense hydrogen over a broad range of parameters. In particular, we have presented the first species-resolved results for the corresponding exchange-correlation kernel, which constitutes a key input for a host of applications.
More recently, we have extended our PIMC simulations to warm dense beryllium. This has allowed us to re-interpret a set of x-ray Thomson scattering (XRTS) measurements taken at the National Ignition Facility (NIF) in Livermore, California, leading to an unprecedented degree of consistency between various aspects of the analysis. Interestingly, the application of our highly accurate PIMC simulations has substantially revised the extracted mass density (by ~30%) compared to previously used chemical models, which has important implications for the modeling of inertial confinement fusion experiments. The diagnostic utility of PIMC simulations for experiments with WDM will be further explored in the upcoming Discovery Science project "Advancing Atomic Physics at GBar Pressure" (PI: Dr. T. Döppner, co-PI: Dr. T. Dornheim) at NIF scheduled for September 2025.
As mentioned above, highly accurate PIMC results constitute an important benchmark for other methods, including density functional theory simulations with various thermal and non-thermal exchange-correlation functionals, average atoms models, chemical models, etc. This has been explored in a number of publications for different materials, conditions and observables. In addition, the PIMC data constitute valuable input e.g. for the extraction of ionization degrees and ionization potential depression, or as the basis for a so-called analytic continuation to compute a dynamic structure factor from an imaginary-time correlation function. The latter aspect is being explored actively in our group, opening up the enticing possibility to present dynamic structure factors of real materials. Moreover, we mention a number of methodological advances regarding the dynamic Matsubara density response.
Finally, we have pursued various aspects of density functional theory simulations, including the systematic benchmarking against PIMC, the development of time-dependent density functional theory set-ups and the computation of density response properties.
More recently, we have extended our PIMC simulations to warm dense beryllium. This has allowed us to re-interpret a set of x-ray Thomson scattering (XRTS) measurements taken at the National Ignition Facility (NIF) in Livermore, California, leading to an unprecedented degree of consistency between various aspects of the analysis. Interestingly, the application of our highly accurate PIMC simulations has substantially revised the extracted mass density (by ~30%) compared to previously used chemical models, which has important implications for the modeling of inertial confinement fusion experiments. The diagnostic utility of PIMC simulations for experiments with WDM will be further explored in the upcoming Discovery Science project "Advancing Atomic Physics at GBar Pressure" (PI: Dr. T. Döppner, co-PI: Dr. T. Dornheim) at NIF scheduled for September 2025.
As mentioned above, highly accurate PIMC results constitute an important benchmark for other methods, including density functional theory simulations with various thermal and non-thermal exchange-correlation functionals, average atoms models, chemical models, etc. This has been explored in a number of publications for different materials, conditions and observables. In addition, the PIMC data constitute valuable input e.g. for the extraction of ionization degrees and ionization potential depression, or as the basis for a so-called analytic continuation to compute a dynamic structure factor from an imaginary-time correlation function. The latter aspect is being explored actively in our group, opening up the enticing possibility to present dynamic structure factors of real materials. Moreover, we mention a number of methodological advances regarding the dynamic Matsubara density response.
Finally, we have pursued various aspects of density functional theory simulations, including the systematic benchmarking against PIMC, the development of time-dependent density functional theory set-ups and the computation of density response properties.
We have presented the first exact results for the species-resolved density response of warm dense hydrogen. This has allowed us to resolve the corresponding exchange-correlation kernels, which is truly unprecedented. The same holds for our highly accurate simulation of warm dense beryllium (without the usual fixed-node approximation), and the utilization of PIMC for the interpretation of WDM experiments.
During the remainder of the project, we will pursue an ambitious complete solution of the notorious sign problem in PIMC, which will require substantial conceptual developments and implementation work. In addition, we will use our capabilities for a broad range of applications, including the benchmarking and development of thermal exchange-correlation functionals for density functional theory, the benchmarking of a host of other WDM methods, and the interpretation and prediction of experiments. Finally, we intend to apply our new capabilities to other research fields beyond the study of warm dense matter, starting with the simulation of ultracold atoms such as normal liquid helium.
During the remainder of the project, we will pursue an ambitious complete solution of the notorious sign problem in PIMC, which will require substantial conceptual developments and implementation work. In addition, we will use our capabilities for a broad range of applications, including the benchmarking and development of thermal exchange-correlation functionals for density functional theory, the benchmarking of a host of other WDM methods, and the interpretation and prediction of experiments. Finally, we intend to apply our new capabilities to other research fields beyond the study of warm dense matter, starting with the simulation of ultracold atoms such as normal liquid helium.