Advocating a new paradigm for electron simulations

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 progress in physics, chemistry, and the materials sciences. Thanks to modern high-performance computer clusters and the establishment of the density functional theory (DFT) simulation method, the researchers were able to change this situation. But even with these tools, the modeled processes are in many cases drastically simplified. Physicists from the Center for Advanced Systems Understanding (CASUS) and the Institute for Radiation Physics at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) have now 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 (DOI: 10.1021/acs.jctc.2c00012).

In the new publication, junior research group leaders Dr. Tobias Dornheim, first author Dr. Zhandos Moldabekov (both CASUS, HZDR) and Dr. Jan Vorberger (Institute for Radiation Physics, HZDR) one of 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. While the basic mathematical equations that describe electronic structures have been known in principle for a long time, they are too complex to solve in practice. Therefore, the actual understanding of, for example, elaborately designed materials has remained very limited.

This unsatisfactory situation has changed with the advent of modern high-performance computing clusters, giving rise to the new field of computational quantum many-body theory. A particularly successful tool here is density functional theory (DFT), which provides 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 suitable for describing many-electron systems. In fact, the number of scientific publications based on DFT calculations has grown exponentially over the past decade, and companies have successfully used the method to calculate the properties of materials more accurately than ever before.

Overcoming a 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, it is still a drastic simplification of processes and a severe limitation.

In their latest publication, the researchers break new ground by extending the DFT method beyond the simplified linear regime. 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 from 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 paper is 1,000 to 10,000 times faster than quantum Monte Carlo calculations,” says Zhandos Moldabekov. “In addition, we were able to show that this is not at the expense of accuracy via temperature regimes from ambient to extreme conditions. The DFT-based methodology of the nonlinear response properties of quantum-correlated electrons opens up the tantalizing possibility to study new nonlinear phenomena in complex materials.”

More possibilities for modern free-electron lasers

“We see that our new methodology fits very well with the possibilities of modern experimental facilities such as the Helmholtz International Beamline for Extreme Fields, which is cooperating with the HZDR and which was recently put into operation,” explains Jan Vorberger. “With high-power lasers and free-electron lasers, we can generate precisely these nonlinear excitations, which 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 in which my newly founded group is moving,” says Tobias Dornheim, who heads the junior research group “Frontiers of Computational Quantum Many-Body Theory”, which was set up in early 2022. “We’ve been mostly active in the high-energy-density 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 number of research areas.”

Publication:
Moldabekov Z, Vorberger J, Dornheim T, Density Functional Theory Perspective on the Nonlinear Response of Correlated Electrons across Temperature Regimes, in Journal of Chemical Theory and Calculation2022 (DOI: 10.1021/acs.jctc.2c00012)

Further information:

dr Tobias Dornheim Young investigator
Center for Advanced Systems Understanding (CASUS) at the HZDR
Email: [email protected]

Media contact:

dr Martin Laqua | Communications, press and public relations officer
Center for Advanced Systems Understanding (CASUS) at the HZDR
Mobile: +49 1512 807 6932 | Email: [email protected]

Through the Center for Advanced Systems Understanding

CASUS was founded in Görlitz/Germany in 2019 and conducts data-intensive interdisciplinary systems research in disciplines as diverse as earth system research, systems biology and materials research. The aim of CASUS is to use innovative methods from mathematics, theoretical systems research, simulations and data and computer science to create digital images of complex systems with unprecedented realism in order to provide answers to pressing social questions. Partners are the Helmholtz Center Dresden-Rossendorf (HZDR), the Helmholtz Center for Environmental Research Leipzig (UFZ), the Max Planck Institute for Molecular Cell Biology and Genetics in Dresden (MPI-CBG), the Technical University of Dresden (TUD) and the University of Wroclaw (UWr). CASUS, run as an institute of the HZDR, is funded by the Federal Ministry of Education and Research (BMBF) and the Saxon State Ministry for Science, Culture and Tourism (SMWK). www.casus.science

The Helmholtz Center Dresden-Rossendorf (HZDR) conducts research – as an independent German research center – in the fields of energy, health and matter. We focus on answering the following questions:

• How can energy and resources be used efficiently, safely and sustainably?

• How can malignant tumors be visualized more precisely, characterized and more

treated effectively?

• How do matter and materials behave under the influence of strong fields and in the smallest dimensions?

To answer these research questions, the HZDR operates large-scale devices that are also used by guest scientists: the Ion Beam Center, the Dresden High Magnetic Field Laboratory and the ELBE Center for High-Power Radiation Sources.

The HZDR is a member of the Helmholtz Association and has six locations (Dresden, Freiberg, Görlitz, Grenoble, Leipzig, Schenefeld near Hamburg) with almost 1,500 employees, including around 670 scientists, including 220 doctorates. candidates.