Theory of Complex Systems and Advanced Materials

Participating Countries and International organizations:

Armenia, Australia, Austria, Azerbaijan, Belarus, Belgium, Brazil, Bulgaria, Canada, Czech Republic, Denmark, Ecuador, Egypt, France, Germany, Hungary, India, Iran, Italy, Japan, Mongolia, New Zealand, Poland, Republic of Korea, Romania, Russia, Serbia, Slovakia, Slovenia, South Africa, Spain, Switzerland, Taiwan, Ukraine, United Kingdom, USA, Uzbekistan, Vietnam.

Issues addressed and main goals of research:

Development of analytical and numerical methods for studying complex many-body systems that are of current interest in modern condensed matter physics, the development of mathematical models of these systems and the identification of universal laws on the example of studied models. Analysis of both lattice and field-theory models of equilibrium and non-equilibrium statistical systems and modeling of a wide class of new materials, including nanostructured materials, which are of great practical importance. The concepts of scaling and universality allow one to go beyond the model approach and to apply the results obtained to broad classes of phenomena studied in the physics of condensed matter. The results obtained will be used in carrying out experimental studies of condensed matter at JINR. It is important to note the markedly growing interdisciplinary nature of research, where condensed matter physics and statistical physics closely intersect with atomic and nuclear physics, particle physics, mathematical physics, astrophysics, and biology.

Expected main results in the current year:

• Development of new methods for studying structural properties of complex systems at nano and micro scales using the small-angle scattering technique. Description of magnetodielectric and magnetorheological effects in smart composite materials.
  
  Modeling of vacancy defects with impurities generated by irradiation with neutrons or heavy ions in HfC_xN_1-x and graphen layers on wolfram slabs for the purpose of comparison with the quantities measured by positron annihilation spectroscopy.
  
  Construction of the theoretical magnetic phase diagram and the spin-wave spectrum of rare-earth magnets YbMgGaO₄ and YbZnGaO₄ in a magnetiс field and comparison with inelastic neutron scattering data.

Calculation of quantum corrections to the spin-wave spectrum of strongly spin-orbit coupled insulator in a magnetic field with in-plane anisotropic interactions.

Calculation of magnon spectral line broadening in a honeycomb ferromagnet with Dzyaloshinskii-Moriya interactions.

Calculation of the electronic spectrum in strongly-correlated electronic systems within the t-J model. Study of the influence of short-range antiferromagnetic correlations on the transformation of the Femi surface topology. Comparison of the obtained results with experiments in hole-doped cuprates.

Calculation of the electronic spectrum and superconductivity temperature as a function of doped holes in the extended t – J model where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account.

Development of new methods for regulating spin reversal in magnetic nanomaterals. Construction of a theory of statistical systems with several coexisting symmetries.

• Investigation of dynamics of collective excitations in the Josephson superconductor-ferromagnet-superconductor nanostructures and their manifestation in the current-voltage characteristics of these systems.

Calculation of the electron mobility and conductivity of polycrystalline graphene.

Investigation of the electron transport in nanostructures based on modern materials such as transition metal chalcogenides and graphene, taking into account the effect of scattering by phonons and the role of the surface.

Investigation of electronic transport properties of molybdenum disulphide monolayer with randomly distributed and periodic antidots in the band and hopping transport regimes.

Investigation of a novel type of superconductivity that emerges in the 3-band Hubbard model on the lattices featuring a topological flat band. Application of this approach to account for high-temperature superconductivity in CuO₂ geometry.

• Finding of connections between the 6j-symbols of the group SL(2,C) with the degenerate cases of superconformal indices of four-dimensional field theories and partition functions of three-dimensional field theories on curved manifolds.
  
  Construction of superconformal indices related to field theories on lens space.

Description of stochastic models of interacting particles with pairing on a one-dimensional lattice. Construction of the Green function and characterization of limiting hydrodynamics and characteristic fluctuations with the help of the Bethe ansatz and free-fermion techniques.

Description of the statistics of loops in the critical percolation model on a cylinder using techniques based on the Temperley-Lieb algebra representations and the Bethe ansatz.

Finding of stochastic dualities in the models of interacting particles based on the properties of the Hecke algebras and their representations.

Investigation of "entangled states” of a complex quantum system when the entire system is in a well-defined state but subsystems are not.

Cosntruction of the quasi-oscillator representation of linear quantum groups: construction of the finite-dimensional representations and investigation of the Hopf structures.

Finding of polynomial solutions of the finite-difference Knizhnik-Zamolodchikov equations related to the diffusion-annihilation stochastic processes. Description of duality functions for these processes.

Collaboration