arXiv subjects

Taras Verkholyak

Publications and source records attributed to Taras Verkholyak.

At least 19 recordsLinked to original sources

arXiv2026

Approaching Kasteleyn transition in frustrated quantum Heisenberg antiferromagnets

We show that the Kasteleyn transition, the abrupt proliferation of infinite strings of defects in classical dimer and related models, can also be relevant for frustrated 2d quantum magnets. This is explicitly demonstrated in a phase of the spin-1/2 Heisenberg diamond-decorated honeycomb lattice where a family of exact eigenstates built as products of dimer and plaquette singlets can be mapped onto the dimer coverings of the honeycomb lattice. The low-temperature properties of this phase are accurately described by an effective dimer model with anisotropic activities and a small, tunable density of monomers, leading to an arbitrarily sharp crossover version of the Kasteleyn transition. The generalization to other geometries and the possibility to realize this model in organo-metallic compounds are briefly discussed.

cond-mat.stat-mech↗

arXiv2026

Manipulation of electromagnetic wave propagation in quantum-spin-chain medium

We consider a simple model of one-dimensional magnetic crystal and examine the propagation of an electromagnetic wave through such a medium. Calculating the dispersion relation ${\bf k}(ω)$ allows us to illustrate how the spread of the electromagnetic wave can be controlled by an external magnetic field. Our rigorous calculations should be useful for more realistic (and less tractable mathematically) models of magnetic media.

cond-mat.str-el↗

arXiv2025

Thermodynamic properties of the macroscopically degenerate tetramer-dimer phase of the spin-1/2 Heisenberg model on the diamond-decorated square lattice

The spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in the presence of a magnetic field displays various quantum phases including the Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, and spin-canted phases, in addition to the trivial fully saturated state. Thermodynamic properties of this model are investigated using several complementary analytical and numerical methods such as exact diagonalization up to the systems of 40 spins, an effective monomer-dimer description, sign-problem-free quantum Monte Carlo simulations for up to 180 spins, and a decoupling approximation. Our particular attention is focused on the parameter region favoring the dimer-tetramer phase. This ground state can be represented by a classical hard-dimer model on the square lattice and retains a macroscopic degeneracy even under a magnetic field. However, the description of the low-temperature thermodynamics close to the boundary between the macroscopically degenerate dimer-tetramer and the non-degenerate monomer-dimer phases requires an extended classical monomer-dimer lattice-gas model. Anomalous thermodynamic properties emerging in the vicinity of the dimer-tetramer phase are studied in detail. Under the adiabatic demagnetization we detect an enhanced magnetocaloric effect promoting an efficient cooling to absolute zero temperature, provided that the system reaches the dimer-tetramer ground state at zero field.

cond-mat.str-el↗

arXiv2023

Magnetic analogue of liquid-gas phase transition of water: case study of a spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice

The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice exhibits an intriguing temperature-driven phase transition in a magnetic field between a classical ferrimagnetic phase and a quantum monomer-dimer phase. A generalized decoration-iteration transformation accurately maps the considered model to an effective spin-1/2 Ising model on a square lattice with temperature-dependent effective interactions and field, whereby the effective field vanishes at the phase boundary separating the classical ferrimagnetic phase from the quantum monomer-dimer phase. Typical features of the magnetization, magnetic susceptibility and specific heat in the vicinity of discontinuous and continuous thermal phase transitions between the classical ferrimagnetic phase and the quantum monomer-dimer phase are elucidated.

cond-mat.stat-mech↗

arXiv2023

Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field

The thermal phase transitions of a spin-1/2 Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field are investigated using a decoration-iteration transformation and classical Monte Carlo simulations. A generalized decoration-iteration transformation maps this model exactly onto an effective classical Ising model on the square lattice with temperature-dependent effective nearest-neighbor interactions and magnetic field strength. The effective field vanishes along a ground-state phase boundary of the original model, separating a ferrimagnetic and a quantum monomer-dimer phase. At finite temperatures this phase boundary gives rise to an exactly solvable surface of discontinuous (first-order) phase transitions, which terminates in a line of Ising critical points. The existence of discontinuous reentrant phase transitions within a narrow parameter regime is reported and explained in terms of the low-energy excitations from both phases. These exact results, obtained from the mapping to the zero-field effective Ising model are corroborated by classical Monte Carlo simulations of the effective model.

cond-mat.stat-mech↗

arXiv2023

Phases of the spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in a magnetic field

The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization, as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength, as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.

cond-mat.str-el↗

arXiv2023

Optimising nanoporous supercapacitors for heat-to-electricity conversion

Innovative ways of harnessing sustainable energy are needed to meet the world's ever-increasing energy demands. Supercapacitors may contribute, as they can convert waste heat to electricity through cyclic charging and discharging at different temperatures. Herein, we use an analytically-solvable model of a cylindrical pore filled with a single file of ions to identify optimal conditions for heat-to-electricity conversion with supercapacitors. We consider Stirling and Ericsson-like charging cycles and show that the former or latter yields more work when a supercapacitor operates under charge or voltage limitations, respectively. Both cycles yield the most work for pores almost as narrow as the size of the ions they contain, as is the case for energy storage with supercapacitors. In contrast to energy storage, which can be maximised by ionophobic pores, such pores do not yield the best heat-to-electricity conversion, independently of the applied potential. Instead, we find that for a given pore size, a moderately ionophilic pore harvests more work than ionophobic and strongly ionophilic pores.

cond-mat.soft↗

arXiv2021

Capacitive energy storage in single-file pores: Exactly-solvable models and simulations

Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion, water desalination, etc. Exactly-solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly-solvable, one-dimensional off-lattice model for charging single-file pores. Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, cation-anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, $C \sim u^{-2}$. This dependence follows from hard-core interactions and is not captured by the lattice model.

cond-mat.soft↗

arXiv2021

Modified strong-coupling treatment of a spin-1/2 Heisenberg trimerized chain developed from the exactly solved Ising-Heisenberg diamond chain

Quantum spin-1/2 antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the novel many-body perturbation expansion, which is developed from the exactly solved spin-1/2 Ising-Heisenberg diamond chain preserving correlations between all interacting spins of the trimerized chain unlike the standard perturbation scheme developed on the grounds of noninteracting spin monomers and dimers. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound Cu$_3$(P$_2$O$_6$OH)$_2$ affording its experimental realization. Within the modified strong-coupling method we have obtained the effective Hamiltonians for the magnetic-field range from zero to one-third plateau, and from one-third plateau to the saturation magnetization. The second-order perturbation theory shows reliable results even for the moderate ratio between weaker dimer-monomer and stronger intradimer coupling constants. We have also examined thermodynamic properties and recovered the low-temperature peak in the specific heat. The accuracy of the developed method is tested through a comparison with numerical density-matrix renormalization group and quantum Monte Carlo simulations. Using the results for the effective Hamiltonian we suggest straightforward procedure for finding the microscopic parameters of one-dimensional trimerized magnetic compounds with strong intradimer and weak monomer-dimer couplings. We found the refined values for the coupling constants of Cu$_3$(P$_2$O$_6$OH)$_2$ by matching the theoretical results with the available experimental data for the magnetization and magnetic susceptibility in a wide range of temperatures and magnetic fields.

cond-mat.stat-mech↗

arXiv2020

Spin-1/2 $XX$ chain in a transverse field with regularly alternating $g$-factors: Static and dynamic properties

We consider the spin-1/2 isotropic $XY$ chain in an external magnetic field directed along $z$ axis with periodically varying $g$-factors. To reveal the effects of regularly alternating $g$-factors, we calculate various static and dynamic equilibrium quantities in the ground state and at finite temperatures. We demonstrate that because of the regularly alternating $g$-factors the saturation field may disappear and the field dependence of the susceptibility in the ground state has additional logarithmic singularity at zero field. Moreover, the zero-field susceptibility has a logarithmic singularity as $T\to 0$. Furthermore, the dynamic structure factors exhibit much more structure in the "wave vector -- frequency" plane that can be traced out to modifications of the two-fermion excitation continua which exclusively determine $S_{zz}(κ,ω)$ and dominate the properties of $S_{xx}(κ,ω)$. We discuss what changes can be observed in dynamic experiments on the corresponding substances.

cond-mat.str-el↗

arXiv2019

Enhanced magnetoelectric effect near a field-driven zero-temperature quantum phase transition of the spin-1/2 Heisenberg-Ising ladder

Magnetoelectric effect of the spin-1/2 Heisenberg-Ising ladder in a presence of the external electric and magnetic fields is rigorously examined by taking into account Katsura-Nagaosa-Balatsky mechanism. It is shown that the applied electric field may control a quantum phase transition between the Néel (stripy) ordered phase and the disordered paramagnetic phase. The staggered magnetization vanishes according to a power law with the Ising-type critical exponent 1/8, the electric polarization exhibits a weak singularity and the dielectric susceptibility shows a logarithmic divergence at this particular quantum phase transition. The external electric field may alternatively invoke a discontinuous phase transition accompanied with abrupt jumps of the dielectric polarization and susceptibility on assumption that the external magnetic field becomes nonzero.

cond-mat.stat-mech↗

arXiv2019

Cluster-based Haldane phases, bound magnon crystals and quantum spin liquids of a mixed spin-1 and spin-1/2 Heisenberg octahedral chain

The mixed spin-1 and spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric spin-1 sites and square-plaquette spin-1/2 sites is investigated using variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The investigated model has in a magnetic field an extraordinarily rich ground-state phase diagram, which includes the uniform and cluster-based Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, two quantum spin liquids and two bound magnon crystals in addition to the fully polarized ferromagnetic phase. The lowest-energy eigenstates in a highly-frustrated parameter region belong to flat bands and hence, low-temperature thermodynamics above the bound magnon-crystal ground states can be satisfactorily described within the localized-magnon approach. The variational method provides an exact evidence for the magnon-crystal phase with a character of the monomer-tetramer ground state at zero field, while another magnon-crystal phase with a single bound magnon at each square plaquette is found in a high-field region. A diversity of quantum ground states gives rise to manifold zero-temperature magnetization curves, which may involve up to four wide intermediate plateaus at zero, one-sixth, one-third and two-thirds of the saturation magnetization, two quantum spin-liquid regions and two tiny plateaus at one-ninth and one-twelfth of the saturation magnetization corresponding to the fragmentized cluster-based Haldane phases.

cond-mat.stat-mech↗

arXiv2019

Spin-1/2 XY chain magnetoelectric: effect of zigzag geometry

A spin-1/2 $XY$ chain model of magnetoelectric on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. By non-uniform spin-rotations the model is reduced to a dimerized $XY$ chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model, zero and finite temperature magnetoelectric effect, obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.

cond-mat.str-el↗

arXiv2017

Magnetic signatures of quantum critical points of the ferrimagnetic mixed spin-(1/2, S) Heisenberg chains at finite temperatures

Magnetic properties of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S = 1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zero-temperature magnetization data obtained within density-matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped Lieb-Mattis ferrimagnetic phase and Tomonaga-Luttinger spin-liquid phase, respectively. While a square-root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data provide a stronger evidence of the quantum critical points at finite temperatures through marked local maxima and minima, respectively.

cond-mat.stat-mech↗

arXiv2017

Magnetization process and low-temperature thermodynamics of a spin-1/2 Heisenberg octahedral chain

Low-temperature magnetization curves and thermodynamics of a spin-1/2 Heisenberg octahedral chain with the intraplaquette and monomer-plaquette interactions are examined within a two-component lattice-gas model of hard-core monomers, which takes into account all low-lying energy modes in a highly frustrated parameter space involving the monomer-tetramer, localized many-magnon and fully polarized ground states. It is shown that the developed lattice-gas model satisfactorily describes all pronounced features of the low-temperature magnetization process and the magneto-thermodynamics such as abrupt changes of the isothermal magnetization curves, a double-peak structure of the specific heat or a giant magnetocaloric effect.

cond-mat.stat-mech↗

arXiv2017

Diversity of quantum ground states and quantum phase transitions of a spin-1/2 Heisenberg octahedral chain

The spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The model belongs to the class of flat-band systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase and two different spin-liquid phases. If the intra-plaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides an exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifth and three-fifth of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in a vicinity of discontinuous quantum phase transitions.

cond-mat.stat-mech↗

arXiv2016

Fractional magnetization plateaux of the spin-1/2 Heisenberg orthogonal-dimer chain revisited: strong-coupling approach developed from the exactly solved Ising-Heisenberg model

The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaux at zero, one-quarter and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gapless Luttinger spin-liquid phase. It is evidenced that the approximate results obtained from the strong-coupling approach are in an excellent agreement with the state-of-the-art numerical data obtained for the spin-1/2 Heisenberg orthogonal-dimer chain within the exact diagonalization and density-matrix renormalization group method. The nature of individual quantum ground states is comprehensively studied within the developed perturbation theory.

cond-mat.str-el↗

arXiv2015

Magnetism-driven ferroelectricity in spin-1/2 $XY$ chains

We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechanism within the frames of exactly solvable spin-1/2 $XY$ chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic or/and electric field.

cond-mat.str-el↗