Research in theoretical physics is devoted to several problems in statistical physics and theory of condensed matter, for instance, phase transitions and critical behavior, development of analytical and numerical methods to study magnetic properties and elastic properties of crystalline and disordered materials, magnetic properties of low-dimensional structures and molecular magnetic materials, study of geometrically frustrated spin systems, application of statistical techniques in economy (econophysics), and study of turbulence by means of quantum field theory.

The astrophysical research specializes in the study of intermediate polars, focusing on the manifestations of their activity in the optical and X-rays, the study of physical processes in interacting binaries (symbiotic and cataclysmic variable stars, contact and near-contact binaries), especially on mechanisms related to mass transfer between the components of these binaries that cause the observed activity of these objects.

Projects:

EXOTIC QUANTUM STATES OF LOW-DIMENSIONAL SPIN AND ELECTRON SYSTEMS (APVV-16-0186)
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The project is devoted to theoretical study of low-dimensional quantum spin and electron systems, which will be examined by the combination of advanced analytical and numerical methods including among other matters exact mapping transformations, transfer-matrix method, strong-coupling approach, classical and quantum Monte Carlo simulations, exact diagonalization and density-matrix renormalization group method. The obtained theoretical outcomes will contribute to a deeper understanding of exotic quantum states of spin and electron systems such as being for instance different kinds of quantum spin liquids as well as quantum states with a subtle long-range order of topological character or with a character of valence-bond solid. The project will significantly contribute to a clarification of unconventional magnetic behavior of selected low-dimensional magnetic materials and thus, it will have significant impact on a current state-of-the-art in the field of condensed matter physics and material science. On the other hand, a detailed investigation of quantum entanglement will establish borders of applicability of the studied spin and electron systems for the sake of quantum computation and quantum information processing. Another important outcome of the project is to clarify nontrivial symmetries in tensor states of the strongly correlated spin and electron systems affected by either position dependent interactions or changes in lattice geometries, which induce phase transitions of many types.

MAGNETOELECTRIC AND MAGNETOCALORIC EFFECT IN EXACTLY SOLVABLE LATTICE-STATISTICAL MODELS (VEGA 1/0043/16)
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Magnetoelectric and magnetocaloric effects will be examined in detail with the help of exactly solvable lattice-statistical models including Ising spin systems, Ising-Heisenberg spin systems and coupled spin-electron systems, which consist of localized Ising spins and delocalized electrons. The primary goal of the project is to explore an influence of external electric field on basic magnetic properties and an influence of external magnetic field on basic thermodynamic properties of the studied lattice-statistical models. A response of magnetic system on a change of external electric and magnetic fields will be investigated mainly in a vicinity of phase transitions (including quantum ones), where particularly interesting behaviour can be expected. The rigorous theoretical results will contribute to a deeper understanding of both studied cooperative phenomena, what enables to propose a subsequent optimalization of technologically important properties of multifunctional materials and magnetic refrigerants.

IMPLEMENTATION OF ELECTRONIC STRUCTURE METHODS IN STUDY OF QUANTUM MATERIALS (MS SR 90/CVTISR/2018)
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Aim of the project is to incorporate in a long-term perspective state-of-the-art research techniques of electronic structure calculations of quantum materials in existing portfolio of research activities at Department of Theoretical Physics and Astrophysics. The project aspire to enlarge field of research study involving recent topics of interlacing of electronic wave function and topological aspects in solids. Recent examples are quantum Hall effect, topological insulators, and topological superconductors characterized by nontrivial topologies of Hilbert space. The project considers most fundamental interactions in description of electronic structure, for instance, spin-orbit coupling which is as a key fundamental interaction allowing to manipulate spin of electrons — essential for spintronics applications. Direct manifestation of the quantum mechanics in solids are electrical polarization or magnetism opening miscellaneous properties of novel functional materials.