Victor Slavin

• Head of Department at National Academy of Sciences of Ukraine

The new class of exactly solvable models of one-dimensional spin chains is found. Interactions of spins with crystalline electric fields (CEF) and spin-spin coupling between neighboring sites are taken into account for those models. Spin-spin coupling includes higher-order spin operators (the Stevens operators) and describes the interaction between...

We consider the spin-1/2 chain material. It was predicted earlier that the intersite spin nematic order can be realized due to the spin-elastic coupling in such a system. Here we show that intersite spin nematic ordered states can be studied using magnetoelastic and magnetoelectric experiments. Intersite spin nematic phases and phase transitions in...

We present numerical and analytical results on the formation and stability of a family of fixed points of deep neural networks (DNNs). Such fixed points appear in a class of DNNs when dimensions of input and output vectors are the same. We demonstrate examples of applications of such networks in supervised, semi-supervised and unsupervised learning...

We have studied the peculiarities of electron transport in one-dimensional disordered chain at the presence of correlations between on-site interaction and tunneling integrals. In the considered models, the disorder in host-lattice sites positions is caused by presence of defects, impurities, existence of electron-phonon interaction, etc. It is sho...

Piezoelectricity in quantum rare-earth metallic boron oxides with the coupling between magnetic, electric and elastic subsystem is studied theoretically. It is proved that the change of piezoelectric modules of the considered crystals are proportional to components of the quadrupole susceptibility, which determines the external magnetic and electri...

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1≪L≲N. A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N→∞, then an asymptotic analysis of the entanglement...

The giant electro- and elastocaloric effects in spin-chain materials are predicted. The theory is based on the exact quantum mechanical solution of the problem. It is shown that the giant jumps in the entropy and the temperature caused by the caloric effect are weakly affected by the initial temperature. The effect can be used for the cooling of ne...

The giant electro- and elasto-caloric effects in spin chain materials are predicted. The theory is based on the exact quantum mechanical solution of the problem. It is shown that the giant jumps in the entropy and the temperature caused by the caloric effect are weakly affected by the initial temperature. The effect can be used for the cooling of n...

The renormalization of the electric permittivity of rare-earth aluminium borates is studied theoretically from the first principles. It is shown how the electric permittivity depends on the external magnetic field and temperature for several compounds of rare-earth ions of that class.

We consider a quantum system of large size $N$ and its subsystem of size $L$ assuming that $N$ is much larger than $L$, which can also be sufficiently large, i.e., $1 \ll L \lesssim N $. A widely accepted mathematical version of this heuristic inequality is the asymptotic regime of successive limits: first the macroscopic limit $N \to \infty$, then...

A spin-1/2 chain system coupled to the elastic subsystem of the crystal is considered. Due to that coupling, the intersite spin nematic ordering in the spin subsystem takes place. The phase transition to the ordered phase is studied using the exact quantum-mechanical approach. It is shown how the nonzero temperature and the external magnetic field...

Using the Kramers–Wannier transfer matrix method, we studied several decorated Ising chains. The exact expressions for thermodynamic characteristics, including the ground state characteristics, were obtained. We considered several modeling chains with different signs and absolute values of exchange constants for the nearest- and the next-nearest ne...

We consider the quantum paramagnet with the coupling between spin and electric degrees of freedom. The dynamical electric characteristics of the system under the action of the ac electric field are calculated. It is shown that for the closed system the quadrupole spin moment oscillates with the frequency of the ac field. The oscillations are modula...

Using the exact Bethe ansatz solution, a one-dimensional correlated electron system coupled to the lattice is considered. Electrons belonging to two orbital bands interact via the exchange coupling. It is shown that the coupling to the lattice strains can produce a phase transition to the state in which the degeneracy in the orbital filling is remo...

Spin-1 chain material is considered. Recently, it was predicted that the spin nematic ordered phase can be realized due to the spin-elastic coupling. In this study we show that the appearance of the spin nematic ordering and phase transitions to such ordered states can be studied using magneto-acoustic experiments. One can observe such phases and p...

We predict the instability of the quantum spin-1 chain material with respect to the spin nematic ordering. For the spin subsystem the spin nematic order parameter is related to the onset of single-ion spin anisotropy. The ordering is caused by the coupling to the elastic subsystem of the crystal or, for spin-1 ultracold bosons in a one-dimensional...

We study the eigenvalue distribution of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the analog of the population covariance matrix is now a function of random data matrices (synaptic weight matrices in the deep neural...

Using exact diagonalization, the density matrix renormalization group approach and the quantum Monte‐Carlo method, we studied the peculiarities of the magnetization profiles and the possibility of spin switching for the Heisenberg spin models of low‐dimensional composite magnets formed by graphene nanoclusters and complex transition‐metal compounds...

We studied the ground state properties of frustrated two-leg ladders in the framework of Heisenberg model. We considered the models of these ladders with all site spins s = 1/2 and the models with different values of spins on neighbor rungs. We found a quantum phase transition mediated by the value of the interactions between the neighbor rungs. Fo...

The exact diagonalization (ED) approach and Quantum Monte-Carlo (QMC) method were used for the study of the lowest energy states and low-temperature magnetic properties of some disordered 1D Heisenberg spin-1/2 systems formed by two types of three-spin structural units. For the system with a singlet ground state and the random distribution of struc...

We review one-dimensional lattice models and the corresponding results that describe the low-temperature properties of quasi-one-dimensional lattice systems with long-range interaction. A widely known example is narrow-band low-dimensional conductors with long-range interelectron repulsion. The models deal with particles that live on the one-dimens...

A class of frustrated one-dimensional periodic Heisenberg spin systems formed either by triangular unit cells with spin 1/2 or by composite unit cells formed by two different structural units, triangles and small linear segments formed by an odd number of spin-1/2 is investigated. Based on perturbative processing and numerical calculations of the d...

We study the distribution of singular values of product of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the population covariance matrices assumed to be non-random or random but independent of the random data matrix in...

Focusing on novel highly correlated low‐dimensional systems, we investigate a class of quasione‐dimensional systems with an even number of spin‐½ sites per unit cell, for which we find, here, that it does not give a gap in the exact excitation spectrum. The unit cells of these systems are formed by two different structural units, each with an odd n...

Spin valves based on materials in which the spin-flip is suppressed by the spatial separation of charge carriers, while maintaining electric neutrality in the valve volume, are considered. The possibility of using these valves as electric batteries is discussed. It is shown that if the potential difference across the valve is controlled, incommensu...

The magnetic properties of narrow zigzag graphene nanoribbons with periodically embedded atoms of transition metals have been studied in the framework of Heisenberg spin Hamiltonian. We have proposed the simple effective model to give a semi-qualitative description of the peculiarities of magnetization profiles of the systems under consideration. T...

Spin valves based on materials in which the spin-flip is suppressed by the spatial separation of charge carriers, while maintaining electric neutrality in the valve volume, are considered. The possibility of using these valves as electric batteries is discussed. Regulating the potential difference on the valve, one can expect the effects of incomme...

Deductive molecular mechanics is applied to study the relative stability and mechanical properties of carbon allotropes containing isolated σ-bonds. Our approach demonstrates the numerical accuracy comparable to that of density-functional theory, but achieved with dramatically lower computational costs. We also show how the relative stability of ca...

Using the density-matrix renormalization group method and quantum Monte Carlo simulation, we studied numerically the energy spectrum and thermodynamics of the quantum Heisenberg spin model for narrow graphene nanoribbons and their derivatives with periodically embedded heteroatoms. For several nanoribbon structures we found macroscopic ground state...

We investigate the spin-Peierls instability of some periodic 1D Heisenberg spin systems having a gapless energy spectrum at different values of coupling J between the unit cells. Using the density-matrix renormalization group method we numerically study the dependence of critical exponents α for the ground-state energies of above spin systems on th...

We have considered discrete one-dimensional Dirac equation in the framework of quantum dimer model with Bernoulli distribution. It has been shown, that superdiffusive transport regime is realized at several combinations of particle mass and amplitude of potential. For the case of non-zero mass it has been shown, that the only one point exists, wher...

Ballistic transport is considered in a channel consisting of two layers under the assumption that the negative refraction of particles moving along the channel occurs on the boundary of the layers; this is similar to the Veselago effect known in optics. This formulation of the model may be defined by electron transport in graphene and Weyl metals,...

We consider the macroscopic system of free lattice fermions in one dimension assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schrödinger operator with independent identically distributed random potential. We show analytically and numerically that the variance of the entanglement entropy of the segment \([-M,M]\)...

We consider the macroscopic system of free lattice fermions in one dimension assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schr\"odinger operator with independent identically distributed random potential. We show analytically and numerically that the variance of the entanglement entropy of the segment $[-M,M]$...

The ground-state structure of one-dimensional electron system on weakly disordered host-lattice (epitaxial substrate) has been studied. It has been shown that long-range correlations in electron system becomes destroyed at arbitrary weak disorder in the positions of host-lattice nodes. We have obtained analytical dependency for typical length, wher...

Explicit formulas for matrix elements of the Hermitian matrix are found through a spectrum of this matrix and spectra of some number of its perturbations. A dependence of sufficient number of perturbations from the structure of the matrix and the kind of perturbations is established. It is shown that for arbitrary matrix needed number of perturbati...

Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m * = m/m sat = 1/4, 1/3, and 1/2...

We study theoretically and numerically the entanglement entropy of the d-dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy ⟨S_{Λ}⟩ of the d dimension cube Λ of side length l admits the area law scal...

We study theoretically and numerically the entanglement entropy of the $d$-dimensional free fermions whose one body Hamiltonian is the Anderson model. Using basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy $\langle S_\Lambda \rangle$ of the $d$ dimension cube $\Lambda$ of side lengt...

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (dom...

The ground state of interacting particles on a disordered one-dimensional host-lattice is studied by a direct numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal, replacing it by the sequence of blocks (domains) of part...

A mechanism of destabilization of an electron crystal over liquid helium is described in the case when the confining electric field is below the field required for complete charge compensation. The dependence of the electron crystal stability parameter on the external confining electric field is obtained within the framework of a one-electron model...

The light absorption spectra of the layered semiconductor MnPS 3 are measured in the temperature range 12-160 K, which covers the temperature of magnetic ordering. It is shown that the interband light absorption coefficient can be described well in the frameworks of three-dimensional model for direct allowed transitions, while an increase in temper...

Optical absorption spectra of the layered semiconductor MnPS3 are measured in the temperature range 12-160 K, which covers the magnetic ordering temperature. It is shown that the interband optical absorption coefficient is well described by a model for direct allowed transitions in three-dimensional compounds, while temperature increases lead to an...

Monte Carlo simulation of two-dimensional Shastry–Sutherland lattice has been carried out using heat-bath method. The dependencies of magnetization M on external field H have been obtained in the framework of classical Heisenberg model. In certain interval of exchange parameters ratio the plateau of magnetization corres-ponding to = 1 / 3 M has bee...

The low-temperature thermodynamic properties of a two-dimensional electron gas on a disordered host lattice are studied in the limit of low electron concentration. A novel Monte Carlo simulation algorithm making it possible to study the properties of this system effectively is proposed. Nonzero residual entropy per particle is found and its value i...

The low-temperature thermodynamic properties of two-dimensional electron ensemble on ordered and disordered host lattice are studied numerically by the transfer-matrix method. It is shown that at low temperatures and weak disordering of host lattice site positions a change in chemical potential leads to successive transitions of the system from ord...

The low-temperature thermodynamic properties of a one-dimensional generalized Wigner crystal at arbitrary values of electron density and arbitrary number of interacting electrons are studied. The modified transfer-matrixes method is applied. It is shown that increasing the number of interacting electrons leads to the appearance of more and more fin...

The low-energy spectrum of one-dimensional lattice electron system with long-range inter-electron repulsion is studied at arbitrary electron concentration, ρ. It is established that the value of the gap in this spectrum is an oscillating function of inverse electron concentration. This value tends to zero at ρ = 1/q (q = 1, 2 …), reaching the maxim...

The low-temperature thermodynamics of one-dimensional (1D) Wigner glass on a disordered lattice (WGDOHL), which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the statistical sum as a product of random transfer-matrixes, has...

Measurements of the spectral distribution of the light absorption coefficient in the garnet NaCa2Mn2V3O12 are performed in a wide range of wavelengths. The influence of unpolarized illumination of a crystal on the light absorption spectrum is investigated. A substantial long-lived photoinduced effect is observed at low temperatures. This effect is...

The ground state and low-temperature thermodynamic properties of a one-dimensional Generalized Wigner crystal on disordered host-lattice have been studied. It is established that the spectrum of elementary excitations has a gapless structure. An instability of the ground state with respect to arbitrary small disordering of host-lattice is revealed....

New numerical methods of the ground state and thermodynamic properties calculations of one-dimensional Generalized Wigner crystal on disordered host-lattice are proposed. Unlike computer simulation methods (for instance, Monte Carlo) these methods bring the exact results. Another attractive feature of the proposed methods is their speed: it is poss...

The low-temperature thermodynamics of a one-dimensional electron gas on a disordered lattice, which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the partition function as a product of random transfer-matrixes, has been deve...

The thermodynamic characteristics of a one-dimensional generalized Wigner crystal are investigated for arbitrary temperature, particle density, and character of the interparticle repulsive pair potential. A method is proposed which permits calculating the partition function of the system with allowance for the interaction between an arbitrary numbe...

The absorption and luminescence excitation spectra of the quasi-one-dimensional antiferromagnet (CMC) doped with copper ions (0–3%) are studied in the temperature range 4.2–80 K. Impurity absorption is detected in crystals: it is weak in the infrared and strong in the ultraviolet (20000–) ranges. The possibility of excitation exchange between the h...

It has been shown that particle ordering into stripes and effective lowering of dimension reside universally in the ground state of two-dimensional lattice systems with a long-range interparticle repulsion for any geometry of the host lattice and any physically reasonable isotropic pair potential. Examples are adatom systems and ensembles of self-l...

In narrow-band conductors a weakly screened Coulomb interelectron repulsion can supress narrow-band electrons' hopping, resulting in formation of a ``frozen'' electron phase which differs principally from any known macroscopic self-localized electron state including the Wigner crystal. In a zero-bandwidth limit the ``frozen'' electron phase is a cl...

It has been shown that effective lowering of dimension underlies ground-state space structure and properties of two-dimensional lattice systems with a long-range interparticle repulsion. On the basis of this fact a rigorous general procedure has been developed to describe the ground state of the systems.

An analysis has been made of strong exciton phosphorescence quenching observed in pure crystals of weak charge transfer (CT) complexes naphthalene-tetrachlorophthalic anhydride (N-TCPA) as well as in those doped with deuteronaphthalene-tetrachlorophthalic anhydride (Nd8-TCPA) (6%) when the temperature is increased from 1.4 to 4.2 K. Quenching of th...

The thermodynamic characteristics of one-dimensional lattice electron systems with long-range interelectron interactions are explicated and studied at arbitrary temperature T and pressure P. Only interactions between neighboring particles are taken into account. Electron-electron correlations are found to be controlled only by the ratio P/T, increa...

The emission decay kinetics and relative quantum yields of exciton luminescence of Cu2+-doped (3%) quasi-one-dimensional antiferromagnetic crystals CsMnCl3⋅2H2O have been studied in the temperature range from 4.2 to 77 K. The experimental emission decay curves have been approximated by the calculated curves obtained using computer simulation of inc...

Computer simulation of incoherent exciton migration in a quasi‐one‐dimensional (q‐1‐D) lattice with randomly distributed traps has been performed. The model assumes both efficient and inefficient exciton trapping. Simulative curves are fitted to the experimental exciton decay curves in q‐1‐D antiferromagnetic crystals CsMnCl3⋅2H2O (CMC) doped with...

The characteristics of low-temperature exciton luminescence in the quasi-one-dimensional antiferromagnet CsMnCl3·2H2O doped with various concentrations of Cu²⁺ impurity ions are investigated. The quasi-one-dimensional migration of optical excitations in the vicinity of an impurity is observed as a result of the spin block being eliminated by distor...

ESR of Gd3+ in Gd2CuO4 at X and Q bands, between 300 and 4K, is presented. The origin of the width and of its thermal changes is shortly discussed.

Pure and doped antiferromagnetic CsMnCl3.2H2O (CMC) crystals have been studied in the temperature range 4.2-300 K. With an increase in temperature the luminescence time and intensity of doped CMC crystals (1% and 0.1% Cu2+) decrease. The exciton-emission quenching is associated with exciton migration and trapping. The emission decay kinetics is app...

The relative contribution of tunneling to the process of overcoming of trap-induced potential barriers by excitons in quasi-one-dimensional dielectrics is considered. The theoretical curve is compared with the experimental temperature dependence of the exciton trapping rate in a quasi-one-dimensional collinear antiferromagnet CsMnCl3 · 2H2O. The po...

An unusual increase of the luminescence relative quantum yield and luminescence decay rate is revealed in quasi-one-dimensional antiferromagnetic crystal CsMnCl32H2O from 6 to 30 K. This effect is related to thermoactivation of the additional exciton-magnon-phonon emission mechanism and takes place in one-dimensional antiferromagnets only. The tran...

The temperature dependence of the relative quantum yield and of luminescence decay kinetics of pure and doped CsMnCl3 · 2H2O (CMC) is studied in the interval 6–300 K. As the temperature increases beyond 60 K, a strong quenching of the exciton glow is observed in the doped crystal (with 0.1% Cu²⁺). Above 60 K, the decay kinetics of doped crystals ha...

The energy migration in the frozen polymer Poly(G) doped with Tb3+ ions-energy traps is studied at 77 K. It is shown that the decay of the Tb3+ luminescence is in good agreement with the theory of migration in low-dimensional systems. The approximation gives the upper limit of the jump rate to be 1.2 × 105 s−1. The influence of the energy disorderi...

The temperature dependence of the relative quantum yield and of luminescence decay kinetics of pure and doped CsMnCl3⋅2H2O (CMC) is studied in the interval 6–300 K. As the temperature increases beyond 60 K, a strong quenching of the exciton glow is observed in the doped crystal (with 0.1% Cu2+). Above 60 K, the decay kinetics of doped crysta...

The relative contribution of tunneling to the process of overcoming of trap-induced potential barriers by excitons in quasi-one-dimensional dielectrics is considered. The theoretical curve is compared with the experimental temperature dependence of the exciton trapping rate in a quasi-one-dimensional collinear antiferromagnet CsMnCl3⋅2H2O. The pote...

Temperature dependences of exciton absorption band half-widths are studied experimentally and theoretically for antiferromagnets with different dimensions of magnetic structures and spin wave spectra. In a 3D AFM with a gapless dispersion of spin waves, the exciton band half-width δ(T)∝T3 In the presence of an energy gap ε˙g in the magnon spectrum,...