Intelligent mathematical tools for the simulation of spin systems can reduce the computing time required for modelling quantum materials on supercomputers. Some of the fastest supercomputers in the world, such as JUWELS (shown in photo), are currently located at Forschungszentrum Jülich in Germany. Photo: Forschungszentrum Jülich/Sascha Kreklau.Supercomputers around the world work around the clock on research problems. In principle, even novel materials can be simulated in computers in order to determine 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.
But 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, which is referred to as the sign problem of the quantum Monte Carlo method.
"The calculation of quantum material characteristics costs about one million hours of CPU on mainframe computers every day," explained Jens Eisert, who heads the joint research group at Freie Universität Berlin and the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB) in Germany. "This is a very considerable proportion of the total available computing time."
Together with his team, Eisert 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," says Dominik Hangleiter from Freie Universität Berlin and first author of a paper on this work in Science Advances. "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 minimized."
For simple solid-state systems with spins, which form what are known as Heisenberg ladders, this approach has allowed 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 such as spintronics that are able to process and store data with considerably less expenditure of energy.
This story is adapted from material from HZB, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.