Plea for a new paradigm for electron simulations Mathematics News

Although most of the basic mathematical equations that describe electronic structures have been known for a long time, they are too complex to solve in practice. This has hampered advances 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. But even with these tools, the modeled processes are simplified considerably in many cases. Today, physicists from the Center for Advanced Systems Understanding (CASUS) and the Institute for Radiation Physics at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) have succeeded in significantly improving the DFT method. This opens up new possibilities for experiments with ultrahigh-intensity lasers, as explained by the group in Journal of Chemical Theory and Calculation.

In the new publication, the leader of the junior research group, Dr. Tobias Dornheim, the lead author, Dr. Zhandos Moldabekov (both CASUS, HZDR) and Dr. Jan Vorberger (Institute for Radiation Physics, HZDR). the most fundamental challenges of our time. : describes exactly how billions of quantum particles interact like electrons. These so-called quantum many-body systems are the focus of many research areas in physics, chemistry, materials science and related disciplines. In fact, most material properties are determined by the complex quantum mechanical behavior of interacting electrons. The basic mathematical equations that describe electronic structures have been known in principle for a long time, but are too complex to solve in practice. Consequently, 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 spawned the new field of computational quantum many-body theory. A particularly successful tool here is density functional theory (DFT), which has provided unprecedented insight into the properties of materials. The DFT is currently considered one of the most important simulation methods in physics, chemistry and materials science. It is particularly adept at describing systems with many electrons. In fact, 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.

Overcome 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 where the (linear) response of the system of interest to an external perturbation such as a laser is measured. In this way, the system can be diagnosed and essential parameters such as density or temperature can be determined. Linear response theory often makes experiments and theories possible in the first place and is almost ubiquitous in physics and related disciplines. However, this is still a drastic simplification of processes and a severe limitation.

In their latest publication, the researchers extend the DFT method beyond the simplified linear regime. With this, for the first time, non-linear effects in quantities such as density waves, braking force and structure factors can be calculated and compared with experimental results of real materials.

Prior to this publication, these nonlinear effects were only reproduced by a set of laborious computational methods, namely quantum Monte Carlo simulations. Although this method gives exact results, it is limited to limited system parameters because it requires a lot of computational power. Therefore, there is 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. “In addition, we were able to show through temperature regimes from ambient to extreme conditions that this is not at the expense of accuracy. The DFT-based methodology of the nonlinear response properties of quantum-correlated electrons opens the exciting possibility to study new nonlinear phenomena in complex materials. »

More possibilities for modern free-electron lasers

“We think that our new methodology fits very well with the possibilities of modern experimental facilities such as the international Helmholtz beamline for extreme fields, in which the HZDR is involved and which was recently put into operation,” explains Jan Vorberger. “With high-power lasers and free-electron lasers, we can generate exactly those nonlinear excitations that we can now study theoretically and investigate with unprecedented temporal and spatial resolution. Theoretical and experimental tools are at hand to study new effects in matter under extreme conditions that were previously inaccessible. »

“This work is a great example to illustrate the direction my newly created group is going,” says Tobias Dornheim, head of the junior research group “Frontiers of Computational Quantum Many-Body Theory”, which was set up in early 2022. has been mostly active in the high energy physics community for the last few years. Now we strive to push the frontiers of science by providing computational solutions to quantum many-body problems in many different contexts. We believe that recent advances in electronic structure theory will be useful to researchers in a range of research areas. »

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