Anisotropic Heisenberg Model Research Articles

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

The effect of a zero-centered Gaussian random magnetic field distribution on the phase transition properties of the anisotropic quantum Heisenberg model has been investigated on a honeycomb lattice within the framework of effective field theory (EFT) for a two-spin cluster (which is abbreviated as EFT-2). Particular attention has been devoted to investigation of the effect of the anisotropy in the exchange interaction on a system with Gaussian random magnetic field distribution. The variation of the critical temperature with the randomness parameter (i.e., the width of the distribution) has been obtained for several anisotropy parameters. Critical Gaussian distribution width values, which make the critical temperature zero, have been obtained. Moreover, it has been concluded that all critical temperatures are of second order, and that reentrant behavior does not exist in the phase diagrams.

Hysteresis behavior of the anisotropic quantum Heisenberg model

The effect of the anisotropy in the exchange interaction on the hysteresis loops within the anisotropic quantum Heisenberg model has been investigated with the effective field theory for two spin cluster. Particular attention has been devoted on the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction for both ferromagnetic and paramagnetic phases.

Bond diluted anisotropic quantum Heisenberg model

Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found.

Tuning interaction strength leads to an ergodic-nonergodic transition of quantum correlations in the anisotropic Heisenberg spin model

We investigate the time dynamics of quantum correlations of the anisotropic Heisenberg model in a time-dependent magnetic field in one-dimensional, ladder, and two-dimensional lattices. We find that quantum correlation measures in the entanglement-separability paradigm are ergodic in these systems irrespective of system parameters. However, information-theoretic quantum correlation measures can also be nonergodic and exhibit a transition from nonergodic to ergodic behavior with the change of interaction strength in the direction of the magnetic field. We also observe that the transition point changes drastically as we go from one-dimensional and ladder lattices to the two-dimensional one.

Bilinear-biquadratic anisotropic Heisenberg model on a triangular lattice

Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value DC, where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.

Magnetic Torque Experiments on TPP[Fe(Pc)L2]2(L = Br and Cl): Antiferromagnetic Short-Range Ordering ofdElectrons, Antiferromagnetic Ordering of π Electrons, and Anisotropy Energy

We have measured the magnetic torque of TPP[Fe(Pc)Br2]2 and TPP[Fe(Pc)Cl2]2 to clarify their magnetic state, comparing our results with those of formerly performed experiments on TPP[Fe(Pc)CN2]2. The conductors in this family exhibit giant negative magnetoresistance. We employed the cantilever magnetometry technique with our newly developed calibration method to obtain absolute values of the torque (J/rad Fe mol), enabling the comparison between experimental and calculated results. With decreasing temperature, the antiferromagnetic ordering of the π electron is found to occur at \({\sim}13\) K, and then the antiferromagnetic short-range ordering of the \(d\) electron follows at \({\sim}8\) K in these two salts. Our anisotropic one-dimensional Heisenberg model can explain 1) the susceptibility data quantitatively, 2) the torque curves quantitatively, which were obtained when the magnetic field was rotated in the \(ac\)-plane, and 3) the behavior of the \(d\) electron in the torque curves qualitatively, whi...

Model study of dissipation in quantum phase transitions

We consider a prototypical system of an infinite range transverse field Ising model coupled to a bosonic bath. By integrating out the bosonic degrees, an effective anisotropic Heisenberg model is obtained for the spin system. The phase diagram of the latter is calculated as a function of coupling to the heat bath and the transverse magnetic field. Collective excitations at low temperatures are assessed within a spin-wave like analysis that exhibits a vanishing energy gap at the quantum critical point. We also discuss the possible realization and application of the model in different physical systems.

Spin transport in the Néel and collinear antiferromagnetic phase of the two dimensional spatial and spin anisotropic Heisenberg model on a square lattice

We analyze and compare the effect of spatial and spin anisotropy on spin conductivity in a two dimensional S=1/2 Heisenberg quantum magnet on a square lattice. We explore the model in both the Neel antiferromagnetic (AF) phase and the collinear antiferromagnetic (CAF) phase. We find that in contrast to the effects of spin anisotropy in the Heisenberg model, spatial anisotropy in the AF phase does not suppress the zero temperature regular part of the spin conductivity in the zero frequency limit - rather it enhances it. We also explore the finite temperature effects on the Drude weight in the AF phase for various spatial and spin anisotropy parameters. We find that the Drude weight goes to zero as the temperature approaches zero. At finite temperatures (within the collision less approximation) enhancing spatial anisotropy increases the Drude weight value and increasing spin anisotropy decreases the Drude weight value. In the CAF phase (within the non-interacting approximation) the zero frequency spin conductivity has a finite value for non-zero values of the spatial anisotropy parameter. In the CAF phase increasing the spatial anisotropy parameter suppresses the regular part of the spin conductivity response at zero frequency. Furthermore, we find that the CAF phase displays a spike in the spin conductivity not seen in the AF phase. Inclusion of the smallest amount of spin anisotropy causes a gap to develop in the spin conductivity response of both the AF and CAF phase. Based on these studies we conclude that materials with spatial anisotropy are better spin conductors than those with spin anisotropy both at zero and finite temperatures. We utilize exchange parameter ratios for real material systems as inputs to the computation of spin conductivity.

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Critical behavior of the 3D anisotropic quantum Heisenberg model in a trimodal random field distribution

Effect of the trimodal random magnetic field distribution on the phase diagrams of the anisotropic quantum Heisenberg model has been investigated for three-dimensional lattices with effective field theory (EFT) for a two spin cluster (which is abbreviated as EFT-2). Variation of the phase diagrams with the random magnetic field distribution parameters has been obtained and the effect of the anisotropy in the exchange interaction on the phase diagrams has been investigated in detail. Particular attention has been devoted on the behavior of the tricritical points with random magnetic field distribution.

Efimov effect in quantum magnets

Physics is said to be universal when it emerges regardless of the underlying microscopic details. A prominent example is the Efimov effect, which predicts the emergence of an infinite tower of three-body bound states obeying discrete scale invariance when the particles interact resonantly. Because of its universality and peculiarity, the Efimov effect has been the subject of extensive research in chemical, atomic, nuclear and particle physics for decades. Here we employ an anisotropic Heisenberg model to show that collective excitations in quantum magnets (magnons) also exhibit the Efimov effect. We locate anisotropy-induced two-magnon resonances, compute binding energies of three magnons and find that they fit into the universal scaling law. We propose several approaches to experimentally realize the Efimov effect in quantum magnets, where the emergent Efimov states of magnons can be observed with commonly used spectroscopic measurements. Our study thus opens up new avenues for universal few-body physics in condensed matter systems.

The critical dynamics of the models of iron–vanadium magnetic superlattice

We report the results of a numerical investigation of static and dynamic critical behavior of the anisotropic easy-plane Heisenberg model which is used as a model for iron–vanadium magnetic superlattices. Models of iron–vanadium magnetic superlattice are investigated with different values of intralayer and interlayer exchange interactions ratio, numerical experiment technique, based on the dynamic finite-size scaling theory. Basic features of the time evolution of dynamic parameters for the researched systems are studied. The effect of interlayer exchange interaction value on the character of critical dynamics is determined. It confirmed the possibility of application of the Hamiltonian with strong easy-plane anisotropy for investigation of both static and dynamic critical behavior of complex planar magnetic models.

Magnetization-based assessment of correlation energy in canted single-chain magnets

We demonstrate numerically that for the strongly anisotropic homometallic S=2 canted single-chain magnet described by the quantum antiferromagnetic Heisenberg model the correlation energy and exchange coupling constant can be directly estimated from the in-field-magnetization profile found along the properly selected crystallographic direction. In the parameter space defined by the spherical angles (\phi, \theta) determining the axes orientation, four regions are identified with different sequences of the characteristic field-dependent magnetization profiles representing the antiferromagnetic, metamagnetic and weak ferromagnetic type behavior. These sequences provide a criterion for the applicability of the anisotropic quantum Heisenberg model to a given experimental system. Our analysis shows that the correlation energy decreases linearly with field and vanishes for a given value H_{cr} which defines a special coordinates in the metamagnetic profile relevant for the zero-field correlation energy and magnetic coupling. For the single-chain magnet formed by the strongly anisotropic manganese(III) acetate meso-tetraphenylporphyrin complexes coupled to the phenylphosphinate ligands, the experimental metamagnetic-type magnetization curve in the c direction yields an accurate estimate of the values of correlation energy \Delta_{\xi}/k_B = 7.93 K and exchange coupling J/k_B=1.20 K.

Spin hydrodynamics in theS=12anisotropic Heisenberg chain

We study the finite-temperature dynamical spin susceptibility of the one-dimensional (generalized) anisotropic Heisenberg model within the hydrodynamic regime of small wave vectors and frequencies. Numerical results are analyzed using the memory function formalism with the central quantity being the spin-current decay rate gamma(q,omega). It is shown that in a generic nonintegrable model the decay rate is finite in the hydrodynamic limit, consistent with normal spin diffusion modes. On the other hand, in the gapless integrable model within the XY regime of anisotropy Delta < 1 the behavior is anomalous with vanishing gamma(q,omega=0) proportional to |q|, in agreement with dissipationless uniform transport. Furthermore, in the integrable system the finite-temperature q = 0 dynamical conductivity sigma(q=0,omega) reveals besides the dissipationless component a regular part with vanishing sigma_{reg}(q=0,omega to 0) to 0.

THE LUTTINGER LIQUID AND INTEGRABLE MODELS

Many fundamental one-dimensional lattice models such as the Heisenberg or the Hubbard model are integrable. For these microscopic models, parameters in the Luttinger liquid theory can often be fixed and parameter-free results at low energies for many physical quantities such as dynamical correlation functions obtained where exact results are still out of reach. Quantum integrable models thus provide an important testing ground for low-energy Luttinger liquid physics. They are, furthermore, also very interesting in their own right and show, for example, peculiar transport and thermalization properties. The consequences of the conservation laws leading to integrability for the structure of the low-energy effective theory have, however, not fully been explored yet. I will discuss the connection between integrability and Luttinger liquid theory here, using the anisotropic Heisenberg model as an example. In particular, I will review the methods which allow to fix free parameters in the Luttinger model with the help of the Bethe ansatz solution. As applications, parameter-free results for the susceptibility in the presence of nonmagnetic impurities, for spin transport, and for the spin-lattice relaxation rate are discussed.

Importance of interplane coupling on the magnetic phases of quasi-two-dimensional tantalites

We propose a three-dimensional model to describe magnetic interactions in a class of tantalite compounds of compositions , with A,A′ = Fe, Co or Ni. Due to the quasi-two-dimensional nature of the magnetism in these compounds, experimental data have been previously interpreted using two-dimensional models. These are anisotropic Heisenberg models or Ising models and include competing exchange interactions from different neighbors. Taking into account all the relevant exchange terms, which include interplane interactions, we show that the latter allows us to understand the various low-temperature magnetic phases observed by neutron diffraction in this family of compounds. This is done by studying the eigenvalues of the exchange-interaction matrix in wavevector space for different sets of coupling parameters, of which those relative to in-plane interactions have been obtained from high-temperature series analysis of the magnetic susceptibility. This approach is rather general and the model presented here is directly applicable to isostructural compounds like ASb2O6.

Frustrated antiferromagnetic spin 1 Heisenberg model with single ion anisotropy on a simple cubic lattice

We study the effects of frustration between nearest, next-nearest neighbor and next-next-nearest neighbors (NNN) of the quantum S=1 anisotropic antiferromagnetic Heisenberg model on a simple cubic lattice with single ion anisotropy using the bond operator technique. We calculate the phase diagram at zero temperature and the gap as a function of temperature in the disordered paramagnetic phase.

Anisotropic frustrated Heisenberg model on the honeycomb lattice

We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size periodic lattices.

Dynamical behavior of vortices in thin film magnetic systems

The origin of the central peak in the neutron scattering function, C(q→,ω), for the classical two-dimensional anisotropic Heisenberg model has been a puzzle for several years. In this work we show that the central peak in the two-dimensional anisotropic Heisenberg model can be explained by a vortex–antivortex number fluctuation due to local diffusion and creation–annihilation processes. This behavior was seen more recently in the dynamics of vortices in magnetic nano-dots. The phenomenology we propose gives the correct behavior for the central peak found in the correlation function C(q→,ω) when compared with experimental as well as numerical spin dynamics results.

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J1–J2–J3 model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.