Although most fundamental mathematical equations describing electronic structures have been known for a long time, they are too complex to solve in practice. This has stifled progress in the physical, chemical, and material sciences. Researchers were able to change this situation thanks to modern high-performance computing clusters and the development of the simulation method density functional theory (DFT).

However, even with these tools, the modeled processes are often greatly simplified. The DFT method has now been significantly improved by physicists at the Center for Advanced Systems Understanding (CASUS) and the Institute of Radiation Physics at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). As the group explains in the Journal of Chemical Theory and Computation, this opens up new possibilities for experiments with ultra-high intensity lasers.

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) take on one of the most fundamental challenges of our time: accurately describing how billions of quantum particles such as electrons interact.

Many research fields in physics, chemistry, material science, and related disciplines are centered on these so-called quantum many-body systems. Indeed, the complex quantum mechanical behavior of interacting electrons determines the majority of material properties. While the fundamental mathematical equations that describe electronic structures have long been known in principle, they are far too complex to solve in practice. As a result, the actual understanding of, say, intricately designed materials has remained very limited.

We see that our new methodology fits very well to the capabilities of modern experimental facilities like the Helmholtz International Beamline for Extreme Fields, which is co-operated by HZDR and went into operation only recently.

Jan Vorberger

With the introduction of modern high-performance computing clusters, this unsatisfactory situation has changed, giving rise to the new field of computational quantum many-body theory. Density functional theory (DFT) is a particularly effective tool in this context, providing unprecedented insights into material properties.

DFT is now widely regarded as one of the most important simulation methods in physics, chemistry, and materials science. It excels at describing multi-electron systems. Indeed, the number of scientific publications based on DFT calculations has grown exponentially over the last decade, and companies have successfully used the method to calculate material properties with unprecedented accuracy.

**Overcoming a drastic simplification**

In the framework of linear response theory, many such properties that can be calculated using DFT are obtained. This concept is also used in many experiments that measure the (linear) response of an interest system to an external perturbation such as a laser. This allows the system to be diagnosed and vital parameters such as density or temperature to be obtained. Linear response theory, which is nearly ubiquitous in physics and related disciplines, frequently makes experiment and theory possible in the first place. However, it is a significant simplification of the processes and a significant limitation.

In their latest publication, the researchers are breaking new ground by extending the DFT method beyond the simplified linear regime. Thus, non-linear effects in quantities like density waves, stopping power, and structure factors can be calculated and compared to experimental results from real materials for the first time.

Prior to this publication these non-linear effects were only reproduced by a set of elaborate calculation methods, namely, quantum Monte Carlo simulations. Although delivering exact results, this method is limited to constrained system parameters, as it requires a lot of computational power. Hence, there has been a big 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 calculations,” says Zhandos Moldabekov.

“Moreover, we were able to demonstrate across temperature regimes ranging from ambient to extreme conditions, that this comes not to the detriment of accuracy. The DFT-based methodology of the non-linear response characteristics of quantum-correlated electrons opens up the enticing possibility to study new non-linear phenomena in complex materials.”

**More opportunities for modern free electron lasers**

“We see that our new methodology fits very well to the capabilities of modern experimental facilities like the Helmholtz International Beamline for Extreme Fields, which is co-operated by HZDR and went into operation only recently,” explains Jan Vorberger. “With high power lasers and free electron lasers we can create exactly these non-linear excitations we can now study theoretically and examine them with unprecedented temporal and spatial resolution. Theoretical and experimental tools are ready to study new effects in matter under extreme conditions that have not been accessible before.”

“This paper is a great example of the direction my recently established group is heading,” says Tobias Dornheim, who leads the Young Investigator Group “Frontiers of Computational Quantum Many-Body Theory,” which was established in early 2022. “In recent years, we have primarily been involved in the high energy density physics community. We are now dedicated to pushing the boundaries of science by providing computational solutions to quantum many-body problems in a variety of contexts. We believe that the current advancement in electronic structure theory will be beneficial to researchers in a variety of fields.”