Participating Countries and International organizations:
Armenia, Australia, Austria, Belarus, Belgium, Brazil, Bulgaria, Canada, Czech Republic, Denmark, Ecuador, Egypt, Finland, 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. Study of a wide range of universal phenomena in complex systems - phase transitions in condensed media and high-energy physics, scaling in (magneto)hydrodynamic turbulence, chemical reactions, percolation, etc. by the methods of quantum field theory including the functional renormalization group. 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 results in the current year:

1. Theoretical and experimental investigations of 3D dense random packing with a power-law size distribution at nano and micro scales.
   
   Simulation of contrast-variation small-angle neutron scattering experiments from biological macromolecules.
   
   Numerical investigation of irradiation resistance of Si-, B- carbides, as well as of HfC_(x)N(_1-x) nonstehiometric compound.
   
   Ab initio estimation of the exchange parameters of Kitaev materials based on transition and rare-earth metals and calculation of their spin-wave spectrum.
   
   Exploration of Kitaev candidate material RuCl₃ and its minimal model.
   
   Calculation of the magnetic phase diagram in strongly-correlated electronic systems within the t-J model for electron doping. Comparison of the obtained results with experiments in the electron-doped cuprates.
   
   Development of a theory of stability for mixtures of quantum fluids.
   
   Elaboration of a model of solids with superfluid dislocations.
   
   Preparation of a review on the models of mixed matter.
   
   Application and development of quantum algorithms for computational problems in condensed matter physics and quantum chemistry.
2. Study of physical phenomena in Josephson nanostructures with ferromagnetic layers.
   
   Development of a model of the Josephson junction coupled to a closed chain of nanomagnets. Study of the possibility of using this junction for determining the state of a chain of nanomagnets.
   
   Investigation of the temperature dependence of the characteristics of various nanostructures such as the band gap, conductivity, and mobility. Application of the frozen phonon method to various modified carbon nanotubes and graphene for determining ways of improvement of their transport characteristics.
   
   Study of the transport properties of quasi-two dimensional polycrystalline Molybdenum disulfide. Investigation of the behavior of electrical resistivity as a function of the transport gap and grain boundary size for different carrier densities.
   
   Study of the topological Hall effect induced by the classical spin background and topological superconductors on the skyrmion lattice using gauge theory.
   
   Investigation of the backscattering of chiral fermions in topological insulators due to rough edges.
    
3. Description of the characteristics of the dimer models on finite-dimensional lattices with different geometries under different boundary conditions. Detailed investigation of the “entangled states” of a complex quantum system with single-ion anisotropy.
   
   Application of the rotor-router model, known as the Eulerian walk, to studying of the dynamics of double-strand breaks of DNA.
   
   Detailed investigation of multidimensional complex hypergeometric integrals in the Mellin-Barnes representation.
   
   Construction of new exactly computable integrals and symmetry transformations for integrals of higher order that are derived by reduction of known relations for elliptic hypergeometric integrals describing superconformal indices in four-dimensional field theories.
   
   Proof of the Derkachov-Manashov hypotheses for the complex Gustafson integrals in the theory of non-compact spin chains.
   
   Construction of a parafermionic generalization of hypergeometric functions and a detailed investigation of the supersymmetric case related to 6j-symbols for supergroups in the Ramond sector as well as in the Neveu-Schwartz sector.
   
   Proof of characteristic identities (i.e., of quantum versions of the Cayley-Hamilton theorem) for a family of orthogonal Quantum Matrix algebras.
   
   Investigation of the quasi-oscillator presentation for the linear quantum groups Uq(gln): construction of finite-dimensional representations and realization of the Hopf structures in terms of the quasi-oscillators.
   
   Construction of nonlocal correlation functions in the branching polymer model near the boundary in the presence of anisotropy.
   
   Classification of Markov dualities in one dimensional integrable stochastic models and two-dimensional lattice models constructed with the use of representations of Hecke algebras of infinite order and their application to solutions of these models.
   
   Evaluation of densities of loops in the O(1) dense loop models and of percolation clusters in critical percolation on the cylindrical lattice of rotated orientation and with an odd circumference.
    
4. Investigation of BEC-BCS crossover in multi-component ultra-cold fermions within the functional renormalization group approach: elucidation of possible phase diagrams and calculation of the respective transition temperatures. Elaboration of an appropriate computational machinery in view of non-perturbative renormalization group flows.
   
   Development of computational methods for calculating the contributions of multi-loop diagrams to the renormalization group functions of dynamic models. Investigation of the dynamics of the superconducting phase transition in low-temperature superconductors.
   
   Investigation of the effects associated with the violation of mirror symmetry in magneto-hydrodynamic developed turbulence. Calculation of two-loop Feynman diagrams generated by the Lorentz force and two-loop diagrams of the response function, leading to an exponential growth of magnetic field fluctuations in the region of large scales. Study of turbulent dynamo.
   
   Construction of field theory models with some effective actions for investigation of chemical reactions of different kinds of particles occurring in random environments. Study of the infrared scaling behavior of statistical correlations of particle densities by renormalization group methods.
   
   Study of isotropic and directed bond percolation. Calculations of three-loop Feynman diagrams generating ultraviolet divergences. Calculation of fixed points of the renormalization group equation and calculation of critical exponents for physically significant and experimentally observable quantities - response functions, density of active nodes (agents), effective radius and mass of active zones.
   
   Study of the effects of isotropic motion of a medium with various statistical characteristics on the possibility of the Hua-Kardara self-organized criticality model to exhibit anisotropic scaling behavior.
   
   Investigation by means of the functional renormalization group method of possible asymptotic regimes corresponding to non-universal scaling behavior of a surface growing in a random media and described by a model including an infinite number of types of interactions.
    

 Collaboration