Case for a New Paradigm for Electron Simulations Mathematics News

Case for a New Paradigm for Electron Simulations Mathematics News

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Although most of the fundamental mathematical equations that describe electronic structures have been known for a long time, they are too complex to be solved in practice. This has hampered progress in physics, chemistry, and materials science. Thanks to modern high-performance computing clusters and the implementation of density functional theory of simulation methods (DFT), researchers have been able to change this situation. However, even with these tools, the modeled processes are in many cases still considerably simplified. Today, physicists from the Center for Advanced Systems Understanding (CASUS) and the Institute for Radiation Physics at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) have managed to significantly improve the DFT method. This opens up new possibilities for experiments with ultra-high intensity lasers, as the group explains in the Journal of Chemical Theory and Computation.

In the new publication, the leader of the group of young researchers, Dr. Tobias Dornheim, the main author, Dr. Zhandos Moldabekov (both CASUS, HZDR) and Dr. Jan Vorberger (Institute of Radiation Physics, HZDR) note the one of the most fundamental challenges of our time. : precisely describing how billions of quantum particles such as electrons interact. These so-called quantum many-body systems are central to many areas of research in physics, chemistry, materials science and related disciplines. Indeed, most material properties are determined by the complex quantum mechanical behavior of interacting electrons. While the fundamental mathematical equations that describe electronic structures have, in principle, been known for a long time, they are too complex to be solved in practice. Consequently, the actual understanding of the materials produced, for example, remained very limited.

This unsatisfactory situation changed with the advent of modern high-performance computing clusters, which gave rise to the new field of computational quantum many-body theory. A particularly successful tool here is Density Functional Theory (DFT), which has yielded unprecedented insights into the properties of materials. DFT is currently considered one of the most important simulation methods in physics, chemistry and materials science. It is particularly adept at describing multi-electron systems. Indeed, the number of scientific publications based on DFT calculations has grown exponentially over the past decade, and companies have used the method to successfully calculate material properties with unprecedented accuracy.

Overcoming drastic simplification

Many such properties that can be calculated using DFT are obtained within the framework of linear response theory. This concept is also used in many experiments in which the (linear) response of the system of interest to an external disturbance such as a laser is measured. This way the system can be diagnosed and essential parameters like density or temperature can be obtained. Linear response theory often makes experiment and theory feasible in the first place and is nearly ubiquitous throughout physics and related disciplines. However, this is still a drastic simplification of the processes and a strong limitation.

In their latest publication, the researchers innovate by extending the DFT method beyond the simplified linear regime. Thus, nonlinear effects in quantities such as density waves, stopping power and structure factors can be calculated and compared for the first time with experimental results of real materials.

Prior to this publication, these nonlinear effects were only reproduced by a set of elaborate computational methods, namely quantum Monte Carlo simulations. Although providing exact results, this method is limited to constrained system parameters, as it requires a lot of computing power. Therefore, there has been a great need for faster simulation methods. “The DFT approach that we present in our article is 1,000 to 10,000 times faster than quantum Monte Carlo calculations,” explains Zhandos Moldabekov. “Furthermore, we were able to demonstrate through temperature regimes ranging from ambient to extreme conditions, that this does not come at the expense of accuracy. The DFT-based methodology of the nonlinear response characteristics of quantum correlated electrons opens the exciting possibility to study new nonlinear phenomena in complex materials. »

More opportunities for modern free-electron lasers

“We find that our new methodology fits very well with the capabilities of modern experimental facilities such as the international Helmholtz beamline for extreme fields, which is co-operated by HZDR and only recently came into operation,” explains Jan Vorberger. “With high-power lasers and free-electron lasers, we can create exactly those nonlinear excitations that we can now theoretically study and examine with unprecedented temporal and spatial resolution. Theoretical and experimental tools are ready to study new effects in matter under extreme conditions which have not been accessible before. »

“This paper is a great example to illustrate the direction in which my newly created group is heading,” says Tobias Dornheim, head of the “Frontiers of Computational Quantum Many-Body Theory” young research group set up in early 2022. “ We have been mainly active in the high energy density physics community in recent years. Now we are dedicated to pushing the frontiers of science by providing computational solutions to quantum many-body problems in many different contexts. We believe that the current advance in electronic structure theory will be useful for researchers in a number of research areas. »

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