Participating Countries and International organizations:
Armenia, Australia, Austria, Azerbaijan, Belarus, Belgium, Brazil, Bulgaria, Canada, Czech Republic, Denmark, Egypt, France, Germany, Hungary, India, Iran, Ireland, Italy, Japan, Mongolia, New Zealand, Poland, Republic of Korea, Romania, Russia, Serbia, Slovakia, Slovenia, South Africa, Spain, Switzerland, Taiwan, Ukraine, 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:

• Studying of superconductivity in the t-J Kitaev model and calculation of the superconducting transition temperature for various parameters of the model.
  
  Calculation of the dc conductivity in the electron-doped cuprate and comparison of the results with experiments performed at the NIC "Kurchatov Institute".
  
  Studying of the relationship between the exchange coupling of rare-earth terbium ions, the electronic and lattice structures of metallic terbium varying under the strong external pressure and comparison of results with experimental data obtained at FLNP, JINR.
  
  Analysis of magnetic interactions between spin-orbit-coupled j=1/2 moments forming structural chains in iridium and rhodium oxides with face-sharing octahedral arrangement.
  
  Structural investigations of multifractals at nano- and micro-scale using the small-angle scattering technique.
  
  Investigation of physical properties of smart polymeric membranes for technical and bio-medical applications.
  
  Investigation of the properties of optical lattices under the increase of intersite interactions.
  
  Development of a method for an efficient regulation of polarization in ferroelectrics.
  
  Calculation of the neutron scattering spectra for a structure of a kagome-strip geometry recently observed in A2Cu5(TeO3)(SO4)3(OH)4 (A=Na, K) for the purpose of a possible experiment proposal for IBR-2.
  
  Calculation and comparison of the spin-wave spectrum on such a lattice with the results of possible neutron scattering experiment.
  
  
• Development of a microscopic theory to describe the experimentally observed transition to the charge density wave phase in the underdoped cuprates.
  
  Investigation of the transport and optical properties of new two-dimensional materials taking into account the effects of disorder.
  
  Investigation of the influence of boundary states and various types of defects on the electronic density of states, electron conductivity and mobility in the monolayer molybdenum disulfide using the real-space Green-Kubo formalism and the non-equilibrium Green function methods.
  
  Study of electron properties of interfaces, such as graphene-fluorographene and graphene-molybdenum disulfide monolayer. Calculation of both the local DOS on the interfaces of structures and the conductance.
  
  Investigation of the electron mobility and conductivity in polycrystalline graphene.
  
  Study of transport properties of Weyl type II semimetal junctions with unconventional superconductors.
  
  Investigation of resonance, chaotic and topological features in Josephson nanostructures with magnetic layers.
  
  Investigation of the possibility of synchronization of the magnetic moments dynamics in a one-dimensional array of nanomagnets coupled to the Josephson junction.
  
  Study of the properties of the electromagnetic pulses propagating through a one dimensional structure consisting of optically active quantum two-level systems.
  
  
• Description of the limit shapes and universal fluctuations of multi-polymer configurations in the model of uniform and weighted spanning forests on the lattice.
  
  Construction of stationary states in the model of interacting particles with generalized exclusion on the segment with open boundary conditions.
  
  Description of interfaces in the dimer models with alternating weights at the bounded domains of planar lattices and characterization of the dependence of their statistics on the shape of the domain.
  
  Obtaining of exact asymptotic expansions of free energy and phase diagrams for dimers on lattices with different geometry and different boundary conditions.
  
  Construction of the Gauss decomposition for the matrix of generators of the Reflection Equation (RE) algebra by means of the spectral extension of the RE-algebra.
  
  Construction of the hyperbolic hypergeometric function connected to the general lens space and investigation of its symmetries, the equation it satisfies and its limiting cases. Investigation of the elliptic analogues of these functions related to superconformal indices of four dimensional field theories.