One of two hundred researchers of the Institute of Physics, a member of the talented younger generation, Jakša Vučičević, PhD, has been trying to solve very complex problems of contemporary physics at the Danube banks in Belgrade, using ingenious procedures. Motivated by a global ambition of solid state physicians to reveal new high-temperature superconductors, Dr Vučičević researches cuprates at the Institute of Physics, on which he has published a series of rather notable papers.

‘Working conditions here do not fundamentally differ from those in top European institutions. In some aspects, it is even better here”, Dr Vučičević notes, comparing the Institute with the French Atomic Energy and Alternative Energies Commission and the Collège de France, which he previously visited. After his postdoctoral studies in France, Dr Vučičević returned to the Institute of Physics, Belgrade, to the Scientific Computing Laboratory. Since 2020, he has been the leader of the *Key2SM *project, which is funded under the PROMIS program of the Science Fund of the Republic of Serbia.

Dr Vučičević is this year’s laureate of the Annual Award of the Institute of Physics, Belgrade, which, as stated in the Panel’s report, was presented to him for his significant contribution to the theory of strongly correlated electron systems through an analytical solution of time integrals in Feynman-diagrams and explanation of mechanisms of Brown-Zak quantum oscillations of conductivity.

The calculations of Dr Vučičević rely on the so-called Hubbard model. It is an approximate model used to describe the transition between conducting systems and insulators. This simple model, common in solid-state physics, describes particles in a periodic potential by neglecting all long-range interactions. The model details the situation at low temperatures and implies that the Hamiltonian has only two terms, which is extremely useful for calculations.

In our new approach to the calculation of dynamic response at a finite temperature, the analytic solution of time integrals in Feynman diagrams, which is a very widespread tool in theoretical physics, is vital. The solution we find is very general, but for the time being, the application is envisaged, first and foremost, within the framework the solid state physics,’ Dr Vučičević explains, discussing the results he has achieved in two previous calendar years. It is this period precisely, that is taken into account for the Annual Award, the award which researchers of the Institute receive on the occasion of the anniversary of the foundation of this institution.

‘We can keep the complete structure of a crystal lattice and all information on atoms that constitute it, but then we largely need to overlook mutual interactions of electrons. The second approach is to observe a pretty simplified lattice with far fewer electrons on lattice clusters, thus mostly preserving their interactions’, explicates Dr Vučičević, adding that the Hubbard model belongs in the second principle. In cuprates, layered materials that are high-temperature superconductors, the interactions have a major role, therefore, this approach yields better results.

‘The Hubbard model is probably a minimal model for the description of mechanisms that are essential to cuprates’ behaviour. However, despite its simplicity, precise solutions are not still available in the most interesting cases,’ states Dr Vučičević, noticing that the future task is to consider more complex models which are to describe the cuprates better and in more detail.

This model is suitable for conductivity studies, since, in cuprates and other materials, where there is a correlated movement of electrons, the simplified description is not possible. According to Dr Vučičević, even if it were possible, it is important to have a description in which longevity is not a parameter of the model, but is derived from the calculations. The interactions are included at the Hubbard model level, and the conductivity can be formally calculated without additional conjectures.

‘It is possible to simulate the Hubbard model in experiments with cold atoms in optical lattices, and there is a new kind of simulator of strongly-correlated systems. These are two-layered hexagonal lattices, such as graphenes and hexagonal boron nitrides’, elaborates Dr Vučiević, adding that recent results of his team have detailed the observations in these two layered lattices.

In these computations, it is not possible to simultaneously treat a large lattice and strong values of interactions, and the second problem is a calculation of dynamic response at a finite temperature.’ This is a several-decade-long problem, and only in 2019 was it discovered that it was possible to skip it, with us being the first who applied this knowledge within the diagrammatic Monte Carlo method’, says Dr Vučičević, expressing hope that this method will enable the determination of the exact conductivity values in the Hubbard model.

According to Dr Vučičević, the physics behind the critical temperature value for superconductivity in cuprates is profound, while the value of a critical temperature itself changes from material to material. ‘To describe the dependence of the critical temperature on the chemical composition and crystal structure of the material, we certainly have to distance ourselves from the simplest Hubbard model,’ explains Dr Vučičević.