Advocating a new paradigm for electron simulations

HIBEF, target cell.

image: The extensive theoretical foundations meet new experimental tools such as those found at the Helmholtz International Beamline for Extreme Fields (HIBEF). Together, effects that were previously out of reach can now be explored.
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Credit: HZDR / Science Communication Lab

Although most of the basic mathematical equations describing electronic structures have been known for a long time, they are too complex to solve in practice. This has hindered progress in physics, chemistry and materials science. Thanks to modern high-performance computer clusters and the creation of the density functional theory (DFT) simulation method, researchers were able to change this situation. But even with these tools, the modeled processes are still drastically simplified in many cases. Now physicists from the Center for Advanced Systems Understanding (CASUS) and the Institute of 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 ultra-high-intensity lasers, as the group explains in the Journal of Chemical Theory and Computation (DOI: 10.1021/acs.jctc.2c00012).

In the new publication, Young Investigator Group Leader Dr. Tobias Dornheim, lead author Dr. Zhandos Moldabekov (both CASUS, HZDR) and Dr. Jan Vorberger (Institute of Radiation Physics, HZDR) tackles one of the most fundamental challenges of our time: to accurately describe how billions of quantum particles such as electrons interact. These so-called quantum many-body systems form the core of many research areas within physics, chemistry, materials science and related disciplines. Indeed, most material properties are determined by the complex quantum mechanical behavior of interacting electrons. Although the fundamental mathematical equations describing 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 been very limited.

This unsatisfactory situation has changed with the advent of modern high-performance computer clusters, leading to the new field of computational quantum many-body theory. Here, a particularly successful tool is density functional theory (DFT), which has provided 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 especially adept at describing systems with many electrons. The number of scientific publications based on DFT calculations has grown exponentially over the past decade, and companies have used the method to calculate the properties of materials as accurately as never before.

Overcoming a drastic simplification

Many such properties that can be calculated with 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 in question to an external disturbance such as a laser is measured. In this way, the system can be diagnosed and essential parameters such as density or temperature can be obtained. Linear response theory often makes experiment and theory feasible in the first place and is nearly ubiquitous in physics and related disciplines. However, it is still a drastic simplification of the processes and a strong 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 of real materials.

Prior to this publication, these nonlinear effects were only reproduced by a series of comprehensive computational methods, namely quantum Monte Carlo simulations. Although this method provides exact results, it is limited to limited system parameters because it requires a lot of computing power. Therefore, there was a great need for faster simulation methods. “The DFT approach we present in our paper is 1,000 to 10,000 times faster than quantum Monte Carlo computations,” says Zhandos Moldabekov. “In addition, we were able to demonstrate that this does not come at the expense of accuracy under different temperature regimes, ranging from ambient to extreme conditions. The DFT-based methodology of the nonlinear response characteristics of quantum correlated electrons opens up the tantalizing opportunity to study novel nonlinear phenomena in complex materials.”

More possibilities for modern free electron lasers

“We see that our new methodology fits very well with the capabilities of modern experimental facilities such as the Helmholtz International Beamline for Extreme Fields, which HZDR is participating in and has only recently been put into use,” explains Jan Vorberger. “With high-power lasers and free electron lasers, we can create exactly these nonlinear excitations that we can now theoretically study and investigate with unprecedented temporal and spatial resolution. Theoretical and experimental tools are poised to study new effects in matter under extreme conditions. conditions that were previously inaccessible.”

“This article is a good example to illustrate the direction my recently created group is taking,” said Tobias Dornheim, head of the Young Investigator Group’s “Frontiers of Computational Quantum Many-Body Theory,” which was installed in early 2022. “We have been mainly active in the high energy density physics community in recent years. Now we are committed to pushing the boundaries of science by providing computational solutions to quantum many-body problems in many different contexts. We believe that the Current advances in electronic structural theory will be useful to researchers in a number of research areas.”

Z. Moldabekov, J. Vorberger, T. Dornheim, Density Functional Theory Perspective on the nonlinear response of correlated electrons across temperature regimes, in Journal of Chemical Theory and Computation2022 (DOI: 10.1021/acs.jctc.2c00012)

More information:

dr. Tobias Dornheim | young researcher
Center for Advanced Systems Understanding (CASUS) at HZDR
Email: [email protected]

Media contact:

dr. Martin Laqua | Communications, Press and Public Relations Officer
Center for Advanced Systems Understanding (CASUS) at HZDR
Mobile phone: +49 1512 807 6932 | Email: [email protected]

About the Center for Advanced Systems Understanding

CASUS was founded in 2019 in Görlitz/Germany and carries out data-intensive interdisciplinary systems research in diverse disciplines such as earth system research, systems biology or 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 of unprecedented fidelity to reality to provide answers to urgent societal questions. Partners are the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), the Helmholtz Center for Environmental Research in Leipzig (UFZ), the Max Planck Institute of Molecular Cell Biology and Genetics in Dresden (MPI-CBG), the Technical University of Dresden (TUD ) and the University of Wroc?aw (UWr). CASUS, managed as an institution of the HZDR, is funded by the German Federal Ministry of Education and Research (BMBF) and the Saxon State Ministry for Science, Culture and Tourism (SMWK).

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

• How can energy and resources be used in an efficient, safe and sustainable way?

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

treated effectively?

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

To help answer these research questions, HZDR operates large-scale facilities, which are also used by visiting researchers: the Ion Beam Center, the Dresden High Magnetic Field Laboratory and the ELBE Center for High-Power Radiation Sources.

HZDR is a member of the Helmholtz Association and has six sites (Dresden, Freiberg, Görlitz, Grenoble, Leipzig, Schenefeld near Hamburg) with nearly 1,500 employees, of whom about 670 are scientists, including 220 Ph.D. candidates.

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