Mathematical tool helps calculate properties of quantum materials more quickly
Intelligent mathematical tools for the simulation of spin systems reduce the computing time required on supercomputers. Some of the fastest supercomputers in the world are currently located at Forschungszentrum Jülich (shown here is JUWELS). © Forschungszentrum Jülich/Sascha Kreklau
Many quantum materials have been nearly impossible to simulate mathematically because the computing time required is too long. Now a joint research group at Freie Universität Berlin and the Helmholtz-Zentrum Berlin (HZB) has demonstrated a way to considerably reduce the computing time. This could accelerate the development of materials for energy-efficient IT technologies of the future.
Supercomputers around the world work around the clock on research problems. In principle, even novel materials can be simulated in computers in order to calculate their magnetic and thermal properties as well as their phase transitions. The gold standard for this kind of modelling is known as the quantum Monte Carlo method.
Wave-Particle Dualism
However, this method has an intrinsic problem: due to the physical wave-particle dualism of quantum systems, each particle in a solid-state compound not only possesses particle-like properties such as mass and momentum, but also wave-like properties such as phase. Interference causes the “waves“ to be superposed on each other, so that they either amplify (add) or cancel (subtract) each other locally. This makes the calculations extremely complex. It is referred to the sign problem of the quantum Monte Carlo method.
Minimisation of the problem
“The calculation of quantum material characteristics costs about one million hours of CPU on mainframe computers every day“, says Prof. Jens Eisert, who heads the joint research group at Freie Universität Berlin and the HZB. “This is a very considerable proportion of the total available computing time.“ Together with his team, the theoretical physicist has now developed a mathematical procedure by which the computational cost of the sign problem can be greatly reduced. “We show that solid-state systems can be viewed from very different perspectives. The sign problem plays a different role in these different perspectives. It is then a matter of dealing with the solid-state system in such a way that the sign problem is minimised“, explains Dominik Hangleiter, first author of the study that has now been published in Science Advances.
From simple spin systems to more complex ones
For simple solid-state systems with spins, which form what are known as Heisenberg ladders, this approach has enabled the team to considerably reduce the computational time for the sign problem. However, the mathematical tool can also be applied to more complex spin systems and promises faster calculation of their properties.
“This provides us with a new method for accelerated development of materials with special spin properties“, says Eisert. These types of materials could find application in future IT technologies for which data must be processed and stored with considerably less expenditure of energy.
Science Advances 2020: Easing the Monte Carlo sign problem; Dominik Hangleiter, Ingo Roth, Daniel Nagaj, Jens Eisert
Doi: 10.1126/sciadv.abb8341
- BESSY II: High-resolution insights into individual biomolecules and catalystsVery small biological samples and even individual biomolecules can now be examined under near-physiological conditions with high confidence at the BESSY II infrared beamline with a newly validated and improved technique: The nanoscale infrared spectroscopy (s-SNOM) with ultra-thin silicon-based membranes. An international team demonstrated after an initial proof of concept, that high-resolution (a few tens of nanometres) nano-IR measurements reliably match expected far-field IR spectra in an aqueous environment. This methodological advance provides a solid foundation for studying biomaterials or observing catalytic processes in a liquid environment.
- New method shows how molecular switches are influenced by their neighborsResearchers at Friedrich Schiller University Jena and the Helmholtz Centre Berlin (HZB) have, for the first time, been able to directly observe how the environment surrounding a molecular switch influences its electronic structure. Molecular switches are molecules that can be switched between two states by external influences such as changes in temperature—similar to a switch with the positions »On« and »Off«. Such molecules are being investigated as potential building blocks for future data storage devices or sensor materials. Using magnetic-field-dependent terahertz spectroscopy, the researchers have now, for the first time, been able to distinguish whether neighbouring molecules in a material are in the same or different states. The results have been published in the journal »Angewandte Chemie International Edition«.
- SEAlab accelerator project completed: Achievements and outlookThe SEAlab accelerator project successfully completed its final measurement campaign in summer 2026. The facility is now being dismantled, with many components set to be reused. The two accelerator physicists, Axel Neumann and Thorsten Kamps, explain what the project has achieved and provide an outlook for the future.