Theory of Complex Systems and Advanced Materials

Participating Countries and International organizations:

Armenia, Australia, Belarus, Brazil, Bulgaria, Canada, Egypt, Finland, France, Germany, India, Iran, Japan, Mongolia, Poland, Romania, Russia, Serbia, Slovakia, South Africa, United Kingdom, USA.

The problem under study and the main purpose of the research:

The most important directions of fundamental research will be theoretical studies of physical phenomena and processes in condensed matter, studies of the properties of new advanced materials, constructing and analysis of theoretical models and the development of analytical and computational methods for their solution. Complex materials such as high-temperature superconductors, magnetic materials, smart composite materials, fractal and layered structures are supposed to be studied and a
wide class of systems with strong electronic correlations will be analyzed. Theoretical research in this area will be aimed at supporting the experimental study of these materials carried out at the Frank Laboratory of Neutron Physics, JINR. It is planned to conduct research in the field of physics of nanostructures and nanomaterials, in particular, using the software packages for modeling physical and chemical processes and for analysis of physical characteristics. First of all, these are modern two-dimensional materials such as graphene, transition metal dichalcogenides, etc., including their modification and chemical functionalization for a subsequent use in the design of new devices for nanoelectronics, spintronics, etc. Partly, these studies are focused on experiments held at the FLNR Center for Applied Physics JINR, Centre “Nanobiophotonics” at FLNP JINR, the Institute of Semiconductor Physics SB RAS and a number of other laboratories of the JINR Member States. The physical properties of stacks of Josephson junctions and various Josephson nanostructures will be studied in detail. Much attention will be paid to the analysis of both lattice and field models of equilibrium and nonequilibrium systems of statistical mechanics. The concepts of scaling and universality allow one to go beyond the model approach and apply the results obtained to broad classes of phenomena studied in the physics of condensed matter. Studies of a wide range of universal phenomena in complex systems - phase transitions in condensed matter 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 are supposed to be carried out.

Brief annotation and scientific rationale:

Enormous recent progress in both the art of sample preparation and the measurement techniques has produced a wealth of high quality data on thermodynamic, transport, structural and spectroscopic properties for new complex materials that exhibit unconventional forms of magnetism, showing evidence for strong electronic and magnetic correlations, or having fractal properties at nano and microscales. These materials attract now considerable attention for various applications, e.g., in quantum computing or in describing the physical and chemical properties of colloids, biological systems, granular materials etc.

Expected results upon completion of the project:
Estimation of the exchange parameters of Kitaev materials based on transition and rare-earth metals and calculation of their spin-wave spectrum.

Magnetic phase diagrams in strongly-correlated electronic systems within the t-J model for electron doping. 

Explaining the structure of systems of dense random packings in nano- and micro-materials. 

Development and application of quantum algorithms for computational problems in condensed matter physics and quantum chemistry. 

Development of a theory of stability for mixtures of quantum fluids. 

Understanding the irradiation resistance of various compounds.

Expected results of the project in the current year:
Estimation of exchange integrals in a novel cobalt-based pyroxene.

Magnon spectrum in a ferromagnetic state of anisotropic-exchange model on a triangular lattice. 

Development of a theory of nonlinear coherent modes in trapped clouds of Bose atoms. 

Analysis of the possibility of generating squeezed and entangled states in optical lattices for quantum information processing. 

Refining the methods of regulating magnetization dynamics in nanomaterials and their application for creating memory devices. 

Dielectric control of Rydberg excitons in atomically thin semiconductors. 

Implementation of quantum algorithms on simulators with classical computing architecture for the numerical study of the electronic and magnetic structures of molecular complexes and crystalline fragments of new functional materials with strong electronic correlations. 

Numerical investigation of the structure of oxides (TiO₂, Sc₂O₃) relevant for nuclear quadrupole interaction experiments. 

Self-consistent calculations of the short-range correlations in trapped Bose gases and the confinement-induced resonances in one and two dimensions.

Correlation properties of dense random packing systems with a power-law distribution of their sizes in thermodynamic limit.

Brief annotation and scientific rationale:

Non-perturbative studies of large-scale systems with many interacting degrees of freedom constitute an important part of modern theoretical physics that has been experiencing a growing interest of researchers during the last decade. Recent advances in this direction are based on the construction and investigation of exactly solvable models of equilibrium and non-equilibrium statistical physics, quantum mechanics and related quantum field theories. Then, with the use of the concepts of scaling and universality the results obtained from the exact solutions can be extended to vast classes of physical phenomena far beyond the realm of such systems. The exact solvability of models of physical systems is provided by their special mathematical structure coined by the term integrability. The models with such a structure is the major subject of studies within the current project.

The project is aimed at further exploration of the field of exactly solvable models of statistical physics, quantum mechanics and quantum field theories, which requires a development of new theoretical tools based on the theory of integrable systems and discovery of new mathematical structures standing behind the exact solvability. The main objectives of the project consist in obtaining exact results about universal laws in interacting particle systems with stochastic dynamics and models of random interface growth, models of equilibrium statistical physics including percolation, polymers and other two-dimensional lattice models and quantum spin chains, studies of known and construction of new types of special functions playing the role of building blocks in the theory of integrable systems and computations of partition functions (superconformal indices), studies of known and construction of new algebraic structures standing behind the integrability concept. 

Expected results upon completion of the project:

Construction and complete classification of one-dimensional stochastic models of interacting particles based on representations of Hecke algebras and related two-dimensional lattice models of interacting paths, as well as obtaining their exact solutions using the Markov duality methods. 

Calculation of exact cluster densities and their asymptotic expansions in percolation models, as well as loop densities in associated densely packed loop models on lattices with different boundary conditions, construction of asymptotic expansions of thermodynamic quantities characterizing the behavior of free-fermionic models on lattices of finite size, such as dimers, Ising model and spanning tree models with different geometry under various boundary conditions. It is also planned to study the boundary behavior of nonlocal correlation functions in models of dense polymers and spanning trees, as well as to describe the limiting forms and universal fluctuations of polymer configurations in these models. 

Application of the studied models of polymers and quantum spin chains to problems from related fields of quantum mechanics and biophysics. Among them are the studies of “entangled states” and magnetic properties of complex quantum spin systems related to the problems of quantum computing, the use of a rotor-router model (Eulerian walks) to study the dynamics of double-stranded DNA breaks. 

Development of mathematical structures behind the integrability. In particular, further study of the properties of elliptic beta integrals and elliptic hypergeometric functions and their various limiting forms, new applications of these functions to quantum field theory, quantum and statistical mechanics and soliton theory, construction of complex hypergeometric functions on root systems in the Mellin-Barnes representation and study of their connections to the two-dimensional conformal field theories. Finding generalized modular transformations for elliptic hypergeometric integrals and description of their consequences for superconformal indices (statistical sums) of four-dimensional supersymmetric field theories. It is also planned to generalize the obtained results to the cases of rarefied hypergeometric functions of various types and describe the relevant physical systems, as well as to investigate connections between soliton solutions of integrable equations, lattice Coulomb gases, non-local Ising chains and ensembles of random matrices. 

Construction and study of new algebraic structures underlying integrability and their use for constructing new integrable systems that could be useful in various applications. Generalization of the Hamilton-Cayley theorem to the case of orthogonal type quantum matrix algebras and study of the subalgebra of spectral values of orthogonal quantum matrices. Construction of an analogue of the Gauss expansion in the reflection equation algebras, and development of the representation theory of these algebras. 

It is also planned to study a series of R-matrix solutions of the braid relation, which make it possible to model stochastic reaction-diffusion processes and study the possibility of constructing new link/knot invariants using new series of R-matrices.

 Expected results of the project in the current year:

Classification of interacting particle systems with stochastic generators based on R-matrix representations of infinite Hecke algebra construction of Markov dualities in them. 

Calculation of exact loop densities on O(1) dense loop model on the infinite cylinder of odd circumference and of related densities of critical percolation clusters in half-turn self-dual percolation. 

Construction and solution of integrable model of lattice paths with partial annihilation. 

Description of the finite-dimensional behavior of a dimer model on a lattice with cylindrical boundary conditions. 

Studies of “entangled states” and magnetic properties of quantum spin chains with single-ion anisotropy and the Dzyaloshinskii-Moriya interaction. 

Application of the rotor-router model (Eulerian walk) to describe the dynamics of recovery of double-stranded DNA breaks. 

Calculation of the ground-state phase diagram, which includes quantum phase transitions, modulation transitions (disorder lines), and the lines of disentanglement, for the dimerized XYZ chain. 

Explanation of cascades of percolation transitions for models of the type of cellular automata or contact processes from the analysis of Lee-Yang zeros of generalized partition functions of stationary states of non-equilibrium models and establishing the relation between the appearance of a critical point of a geometric transition and the properties of the spectrum of the transfer matrix of the corresponding model. 

Construction of a new rarefied elliptic gamma function describing superconformal index of the chiral superfield for the models related to a special series of the lens spaces, as well as computation of the corresponding rarefied elliptic beta integral, which confirms Seiberg duality of the simplest supersymmetric gauge theories on such spaces. 

Construction of the complex hypergeometric integrals on the root systems in the Mellin-Barnes representation, and consideration of the quasiclassical limit for them, connected to the two-dimensional conformal field theory. Investigation of the asymptotics of the Frenkel-Turaevsum, when the parameter of truncation of the corresponding elliptic hypergeometric series N goes to infinity.

Derivation of the Cayley-Hamilton theorem for the family of orthogonal type quantum matrix algebras. Detailed analysis of the spectrum of the quantum orthogonal matrices.

Construction of finite dimensional irreducible representations and investigation of the Hopf structure of the GL-type reflection equation algebras in their quasi-oscillator presentation.

Brief annotation and scientific rationale:

It is planned to conduct research in the field of physics of nanostructures and nanomaterials, in particular, using the software packages for modeling physical and chemical processes and for analysis of physical characteristics. First of all, these are modern two-dimensional materials such as graphene, transition metal dichalcogenides, etc., including their modification and chemical functionalization for a subsequent use in the design of new devices for nanoelectronics, spintronics, etc. Partly, these studies are focused on experiments held at the FLNR Center for Applied Physics JINR, Centre “Nanobiophotonics” at FLNP JINR, the Institute of Semiconductor Physics SB RAS and a number of other laboratories of the JINR Member States. It is planned to analyze topological superconductivity in strongly correlated electronic systems in order to find possible applications for the transmission and storage of quantum information. The physical properties of stacks of Josephson junctions and various Josephson nanostructures will be studied in detail.

The main goal of the project is a theoretical study of the properties of new promising materials, primarily nanostructures and nanomaterials. This is explained not only by the fundamental nature of the physical properties of these materials but also by their practical importance for designing new electronic devices, as well as devices for storing, processing and transmitting information, sensors and biosensors, and others.

Expected results upon completion of the project:
The project is aimed at solving tasks in the following areas: 

in order to identify materials with promising properties for use as a component base for a new generation of electronics, it is planned to study thermal and electron transport in low-dimensional materials of various configurations and chemical composition. An analysis will be made of the role of functionalization, structural modification, the influence of thin layers, polycrystalline, structural defects, and other factors. Experimental studies are carried out in cooperation with the Educational and Scientific Technological Laboratory “Graphene Nanotechnologies” NEFU in Yakutsk (synthesis), the Institute of Semiconductor Physics SB RAS (synthesis, characterization, functionalization), FLNP JINR (chracterization, functionalization, irradiation) and FLNR JINR (ion irradiation to create nanopores). 

Analysis of topological superconductivity in strongly correlated electronic systems in order to search for possible applications for the transmission and storage of quantum information and for the study of non-standard quantum transport that is insensitive to local noise sources. 

Study of dynamic, transport and chaotic phenomena in hybrid Josephson nanostructures with magnetic materials for the purposes of superconducting spintronics. Modeling of quantum phenomena in Josephson qubits (memory elements). 

Study of the properties of polarons in low-dimensional materials and nanostructured objects. Analysis of plasmon-phonon interaction and plasmons in nanoscale and massive objects.

Expected results of the project in the current year:

Study of the interaction of superconductivity and magnetism in Josephson hybrid structures. Analysis of the influence of a domain wall motion in a ferromagnetic layer on the dynamics of solitons in the Josephson junction. Investigation of the interaction of magnetic excitations of the domain wall type with solitons arising in a long Josephson junction.

Study of the influence of temperature on the band structure and transport characteristics in various functionalized nanostructures such as graphene and carbon nanotubes. Analysis of electronic transport properties of 2D systems from density functional band-structure calculations. 

Study of the electronic transport in polycrystalline nanomaterials including graphene. Analysis of the impact of grain boundaries on resistivity in semiconducting and semimetalic materials. 

Study of topological superconductivity induced by strong electron correlation. Analysis of the effect of the strong electron correlation on the properties of the topological superconductor. 

Brief annotation and scientific rationale:

Complex physical phenomena such as developed turbulence, transport phenomena, non-equilibrium phase transitions, percolation, chemical reactions and surface growth in random media are difficult to study theoretically and experimentally; however, in the light of their wide distribution in nature such studies prove themselves to be very valuable. 

The main task of the project will be the formulation of the corresponding theoretical models, which can be investigated using the methods of quantum field theory and non-equilibrium statistical physics. The main goal is to study the statistical characteristics of fluctuating fields in the region of large spatial scales, identify phase transitions and to calculate universal critical exponents and non-universal amplitudes. 

Dynamic nonlinear systems in which non-equilibrium (stochastic) fluctuations of physical quantities play a decisive role, is one of the most important research topics by leading scientific teams in the world. They cover a wide range phenomena, which we observe in the world around us.

Notable examples of stochastic processes include: hydrodynamic and magneto-hydrodynamic turbulence, describing, in particular, turbulent movements in the Earth's atmosphere and oceans, the spread of pollutants in them (including chemically active), as well as chaotic motions of plasma on the surface of the sun and in space. One of the important consequences of the existence of mechanical instabilities in electrically conducting turbulent media is an exponential growth of magnetic fluctuations leading to the formation of observed nonzero averaged magnetic fields only due to the kinetic energy of the turbulent medium. 

Another important example of stochastic systems is percolation processes. They describe phenomena such as seepage in porous media, filtration, spread of infectious diseases, forest fires and others. Their universal feature is the existence of a non-equilibrium phase transition to an inactive (absorbing) state that extinguishes all activity of the observed system. Obviously, the study of transitions between a stationary active and the inactive phase is of great practical importance.

The main object of the study is physical quantities that depend on space-time coordinates and therefore are fluctuating fields, and the measured quantities are their statistical averages. The most important of them are non-zero average field values, response functions, multipoint correlation functions, two-point simultaneous correlations (structural functions), including composite fields (operators). In the region of large spatial and temporal scales, their scaling behavior with universal critical exponents is observed. The analysis of stability regions of scaling regimes and the calculation of indices is a priority goal in the study of stochastic nonlinear systems.

The main goal of the project is to study stochastic nonlinear dynamic systems such as developed (magneto)hydrodynamic turbulence, non-equilibrium phase transitions, phase transitions in systems with high spins, kinetics of chemical reactions, percolation processes, surface growth in random media and self-organized criticality.

Expected results upon completion of the project:

Investigation of the crossover in systems of multicomponent fermions within the BEC-BCS functional renormalization group: analysis of phase diagrams and calculation of transition temperatures to the ordered state. Approbation and adaptation of computational methods for solving non-perturbative equations of the functional renormalization group. 

Development of computational methods for calculating the contributions of multi-loop diagrams to the renormalization group functions of dynamical models. Investigation of the dynamics of the superconducting phase transition in low-temperature superconductors. 

Study 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 the phenomenon of turbulent dynamo.

Construction of effective field-theoretical models of chemical reactions of various types of particles occurring in random media. Study of the infrared scaling behavior of statistical correlations of particle densities by renormalization group methods. 

Study of isotropic and directed percolation. Calculation of multi-loop Feynman diagrams generating ultraviolet divergences. Finding fixed points of the renormalization group equations and calculating 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 effect of isotropic motion of a medium with different statistical characteristics on the possibility of anisotropic scaling in the Hua-Kardar self-organized criticality model. Investigation by the functional renormalization group method of possible asymptotic regimes corresponding to the non-universal scaling behavior of a surface growing in a random environment and described by a model that includes an infinite number of types of interactions.

Expected results of the project in the current year:

Investigation of the superfluid phase transition in the SU(n) symmetric model in the framework of the functional renormalization group at finite temperatures.

Investigation of statistical correlations of magnetic fluctuations in the model of stochastic magnetic hydrodynamics with broken mirror symmetry in the two-loop approximation. Calculation of the value of the spontaneously generated homogeneous mean magnetic field. 

Analysis of the behavior of governing fields in isotropic percolation near the point of second-order phase. Calculations of critical exponents in the two and three-loop approximation. 

Four-loop renormalization group calculations in a stochastic model of devolved turbulence.

Investigation of the effect of medium motion on a system with self-organized criticality described by the stochastic Hua-Kardar model. Finding possible types of critical behavior and the area of their stability. Calculation of the corresponding critical exponents in the leading order of perturbation theory.

Calculation of the critical index of the viscosity coefficient at the transition to the superfluid state within the framework of the generalized model A.