Kharkiv physicists are developing new tools for describing quantum materials

Magnets used in bank cards, access passes and hard disk drives, superconductors found in medical MRI scanners, and semiconductors embedded in every television set – all of these are quantum materials. Yet studying and understanding their properties remains one of the greatest challenges in modern physics. The project “Novel Theoretical Approaches for the In-Depth Description of Correlated Quantum Many-Body Systems”, supported by the National Research Foundation of Ukraine, is aimed precisely at bridging the gap between physical reality and our ability to describe it.

The project PI is Andrii Sotnikov, Leading Researcher at the National Science Centre “Kharkiv Institute of Physics and Technology”.

Why this particular idea?

“Since my student years, I have been fascinated by problems that appear extremely difficult at first glance but have the potential to become a key driver of scientific and technological progress”, says Andrii Sotnikov. Physical models of correlated quantum systems – such as magnetic materials, semiconductor diodes and superconductors – are a prime example of such problems. The phenomena observed in these materials arise from the collective behaviour of billions of elementary particles – electrons, ions and atoms – that move and interact simultaneously with one another and with external fields. In the quantum regime, particles do not occupy precisely defined positions in space, and their collective behaviour gives rise to remarkable effects that are fundamental to modern technologies.

Describing such systems is extraordinarily challenging. Even the most powerful classical computers, using conventional approaches, can accurately simulate a system containing only around 10–20 quantum particles, whereas real materials involve billions of them. Parallelising calculations across supercomputers offers little relief, as this limitation stems from a fundamental exponential growth in computational resources required with each additional quantum degree of freedom. Quantum computers, together with advanced error-correction protocols, could eventually overcome this barrier. However, they are expected to reach sufficient capability only in the 2040s at the earliest.

“We couldn’t just sit and wait”, says the PI. So, in 2024, the young researcher and his colleagues decided to submit the application for grant support, especially as they already had preliminary results and a clear vision of how to develop alternative approaches for the theoretical description of complex quantum systems using classical computational resources.

Better tools for a complex problem

“It is safe to say that nobody really understands quantum mechanics,” the researcher says with a smile, quoting the famous remark by Nobel Prize laureate Richard Feynman. “Despite this, humanity has been actively using its results for the past hundred years and continues to push forward.”

“With the development of quantum technologies, and quantum computers in particular, we are increasingly realising that in modelling quantum systems and the unique properties of materials for present and future technologies, we have a very limited set of tools”, continues Andrii Sotnikov. “As if we were still using a screwdriver to pull out nails, when there should be much more suitable tools available”. The aim of the project is precisely to develop better tools – advanced quantum-mechanical approaches adapted to analytical calculations and to the capabilities of modern classical computers.

In particular, a promising line of research has been the use of tensor networks methods. The essence of this approach lies in representing the wave functions of interacting quantum particles as a network of interconnected mathematical objects – matrices and tensors. Such a representation is at once compact (it can be implemented using classical computers) and sufficiently accurate to capture the quantum-mechanical nature of the system.

According to the PI, tensor networks are currently the main alternative to quantum computers in the modelling of physical systems. Research groups working with tensor networks adapt the corresponding algorithms and, again and again, outperform quantum computers in simulating the physical behaviour of quantum systems. This is supported by results published in leading scientific journals ranked in the first and second quartiles.

Kharkiv Reinforced

The project is scheduled to conclude at the end of 2026 and, despite the challenges of working in a frontline city, the project team is delivering results that exceed the planned indicators. In particular, the researchers have expanded the scope of the project’s core research objectives and prepared additional publications. “I am grateful to the project team for this, especially to the early-career researchers”, emphasises the PI.

Four young project team members have remained in Kharkiv throughout its implementation, working under conditions of constant danger. “It was precisely the ingenuity and ambitious approach of the young researchers that inspired and supported me during psychologically difficult moments”, stressed the researcher.

There were also practical difficulties. Procuring modern equipment for the computing cluster proved far more challenging than expected: the depreciation of the hryvnia and the rising cost of components (such as RAM and graphics processing units) exceeded the 10% inflation buffer included in the budget. Fortunately, the project team managed to find ways to ensure the successful continuation of the project, but, as Andrii Sotnikov notes, conditions on the computer hardware market may make it impossible for similar projects to be implemented by other research groups. Therefore, he believes that grant funding should be increased to account for inflation.

Having a clear idea and a solid plan

“If you have an original and promising idea that is of interest to you and your team, and if you meet the formal requirements of the call for proposals, do not hesitate – submit your application”, advises Andrii Sotnikov to his colleagues. The most important thing is not to postpone the preparation of documents until the final days. It is better to start working on them immediately after the call for proposals is announced, in order to save time for refining the substantive part of the proposal. In collaborative projects, it is essential to distribute tasks among team members in a rational way, to listen to the team’s ideas, and to look at the project through the eyes of a potential reviewer. Experienced reviewers are more likely to award higher scores to achievable plans than to ambitious promises without guarantees of implementation.

Finally, a word about the project team. “I am proud of the level of mutual support within the team”, highlights Andrii Sotnikov. “Kharkiv is truly reinforced!”

 

Interviewed by Svitlana GALATA