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The aim of research project is theoretical understanding of physical mechanisms responsible for the formation of complex (magnetic, orbital, or charge) ordered phases in Mott insulators of various geometries and for the gradual disappearance of these orders as a result of doping. We plan to search for the most favorable physical conditions and interactions responsible for the selected type of behavior/phase. The mechanism of formation of superconducting states in various strongly correlated electron systems will also be investigated. Studies have an interdisciplinary character and will cover some aspects of the physics of cold atoms with the orbital degrees of freedom and the possibilities of quantum model systems for information storage and quantum computations.

The starting point to describe the investigated systems are effective tight binding models of local interactions that lead to strong correlations between electrons. These models will be studied directly in the Hartree-Fock approximation (in order to obtain qualitative results), and methods that take into account the effects of strong electron correlations: variational methods, slave boson mean field and others. Dynamic mean field theory (DMFT) and the cluster DMRG (CDMRG) method, taking into account the dynamics of strongly correlated states, will be applied. To describe a Mott insulator and doped insulators the most modern methods and tools for the description of strongly correlated electron systems will be used, including also those that come up during the project. We will not only use modern quantum methods to describe quantum many-body systems, but also develop new ones. For Mott (or charge-transfer) insulators the effective spin-orbital models will also be derived describing the interactions in these insulators and being a starting point to the corresponding t-J-like models for doped systems. Ground states of these models will be studied using exact diagonalization methods, the density matrix renormalization group (DMRG), cluster mean-field and variational methods. Excited states and dynamics will further be studied with Green's function methods. Development of algorithms and numerical methods useful in studies of strongly correlated systems is anticipated. A special feature of the project is wide international cooperation with world-class experts in the theory of strongly correlated electrons in a few leading centers. Most problems will be solved in international teams with participation of leading experts, which will ensure the best choice of research methods and a high level of and effectiveness of the research. Condition for the success of the project is ongoing scientific cooperation and frequent visits of our project contractors to foreign laboratories and visits of our collaborators from abroad at the Jagiellonian University.

The proposed studies concern real and model systems with strongly correlated electrons. These systems have very interesting properties and can be applied in science and technology, having the specific knowledge of their properties and when the new materials with desired magnetic and transport properties are synthesized. The contribution of orbital degrees of freedom could lead to control of transport properties or to new materials with desirable properties, including functional materials. Obtaining such materials is not planned; the proposed studies are aimed at understanding the physical properties and creating potential opportunities to obtain such materials in the future. Similarly, knowledge of the physical properties of multilayer systems can lead to the controlled synthesis of new superconducting materials. Because the research is partly interdisciplinary, the results may have implications for the development of related fields: the theory of cold atomic gases and quantum methods for data processing and quantum information.

This research is pioneering because it involves the studies of new quantum ordered or disordered phases and the physical conditions necessary for the synthesis of new materials with superconducting properties allowing to control the insulator-metal phase transition and related transport properties by manipulating the spin-orbital order. Low dimensional or layered systems with strongly correlated electrons are poorly understood and it is expected that in several of them new quantum phases, interesting from the standpoint of basic research and in view of future applications, can be found. Our approach is innovative and the cooperation with several foreign centers of excellence in this area is well established.