Anisotropic Heisenberg Model Research Articles

Quantum many‐body phenomena in coupled cavity arrays

AbstractThe increasing level of experimental control over atomic and optical systems gained in recent years has paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of quantum many‐body phenomena, originally encountered only in condensed‐matter physics, and the possibility of experimentally accessing them in a more controlled manner. In this review article we survey recent theoretical studies concerning the use of cavity quantum electrodynamics to create quantum many‐body systems. Based on recent experimental progress in the fabrication of arrays of interacting micro‐cavities and on their coupling to atomic‐like structures in several different physical architectures, we review proposals on the realisation of paradigmatic many‐body models in such systems, such as the Bose‐Hubbard and the anisotropic Heisenberg models. Such arrays of coupled cavities offer interesting properties as simulators of quantum many‐body physics, including the full addressability of individual sites and the accessibility of inhomogeneous models.

Numerical Study on Magnetic Transitions in Double-Layer Spin Lattice Using Anisotropic Heisenberg Model

Monte Carlo simulations have been used to study the magnetic properties of double-layer thin film in Anisotropic Heisenberg Model with different anisotropy and direct exchange parameters, applying Metropolis algorithm. We investigate the antiferromagnetic ordering of the basal layer spins’ influence on the magnetic behavior of the superior layer. The magnetization, out-of-plane and in-plane magnetic susceptibilities, staggered magnetization and also the specific heat behaviors according to temperature are investigated in order to find out the potential magnetic ordered phases and the critical temperatures, for different parameter settings. Taking into account the balance between direct exchange and anisotropy interaction parameters we detect five different magnetic ordering states. These are: ferromagnetism, short-range ferromagnetism, antiferromagnetism, in-plane ordering and paramagnetism, which are characterized by specific properties; and we point also out some different magnetic phase transitions that can appear in the system.

Manganese(III) Compounds of Phenol−Pyrazole-Based Ligands: Synthesis, Crystal Structure, Magnetic, and Thermal Properties

Reaction of H 2 phpzR (R = H, Me, Ph; H 2 phpzH = 3(5)-(2-hydroxyphenyl)pyrazole, H 2 phpzMe = 3(5)-(2-hydroxyphenyl)-5(3)-methylpyrazole, and H 2 phpzPh = 3(5)-(2-hydroxyphenyl)-5(3)-phenylpyrazole)) with MnCl 2 ·2H 2 O or MnBr 2 ·4H 2 O in an acetonitrile-methanol mixture and in the presence of a small quantity of triethylamine affords the compounds [Mn(HphpzR) 2 Cl] (R = H (1), Me (3), and Ph (5) and [Mn(HphpzR) 2 Br] (R = H (2), Me (4), and Ph (6)). This new family of compounds 1-6 with a library of phenol- pyrazole-based ligands was structurally characterized. All compounds are mononuclear manganese(III) coordination compounds in which the manganese(III) ion has a square-pyramidal geometry. In compounds 1-4 intermolecular hydrogen bonds are present between the N-H group of the pyrazole ring of a mononuclear entity and the halogen of a neighboring molecule, thus forming ladder-like chains. The presence of two crystallographically independent molecules in the unit cell of 5 and 6 precludes formation of 1D structure and instead gives rise to a 2D structure with the independent molecules aligned in a face-to-face manner. Low-temperature magnetization studies evidence the presence of antiferromagnetic interactions between the manganese(III) ions in all compounds. Detailed temperature-dependent susceptibility and magnetic specific heat measurements on compounds 1 and 2 show the presence of antiferromagnetic S = 2 chains, the magnetic interaction being described by the anisotropic Heisenberg model with a predominantly planar (XY) type of crystal field anisotropy. In addition, the magnetic specific heat data evidence the occurrence of long-range magnetic ordering between chains in 1 and 2 below about 1.5 K. Compounds 3-6 show weaker antiferromagnetic interactions as compared with 1 and 2.

Neutron scattering investigations of multiferroic YMnO3

Multiferroic materials are the materials that show several cooperative ordering phenomena simultaneously. Here we consider only those materials that show both antiferromagnetism and ferroelectricity and in which the ordering parameters are coupled to each other. I shall review our recent neutron scattering investigations on multiferroic hexagonal manganites YMnO3. We have determined the spin wave dispersions in YMnO3 in symmetry directions by inelastic neutron scattering and have fitted the results with a simple nearest-neighbour anisotropic Heisenberg model. We have investigated the spin dynamics of YMnO3 above TN ∼ 70 K and have shown the existence of persistent albeit heavily damped spin waves.

Renormalized theory of the two-dimensional [formula omitted] dilute spin-wave systems at low temperatures

Due to strong fluctuations, conventional approaches to handling repulsive spin-1/2 spin-waves in three dimensions do not work in low dimensions at temperature T≠0. We have constructed a renormalized theory for the two-dimensional spin-1/2 anisotropic quantum Heisenberg model by means of exact mappings between spin-1/2 systems and their corresponding hard-core Bose–Hubbard systems. With the t-matrix method, hard-core Bose–Hubbard systems can be effectively described by the corresponding soft-core Bose–Hubbard Hamiltonians at low energy. The method of running coupling constant in field theory is used to fix the infrared divergence due to long wavelength fluctuations in low dimensions at T≠0. Our results agree well with previous analytical and numerical works. The method dealing with infinities used by others in 3D is a special case of our renormalization scheme. Our approach works in both two and three dimensions at T=0 and T>0. We think that our renormalization scheme is a more general and systematic approach in condensed matter physics.

Magnetic torque and heat capacity measurements onTPP[Fe(Pc)(CN)2]2

Magnetic torque and heat capacity measurements on TPPFePcCN22 are reported. The torque curves for the magnetic field rotated within the ab plane have a fourfold symmetry, exhibiting inversions around 13 and 27 K. The heat capacity exhibits a broad peak around T=16.5 K. By applying the magnetic field along the c axis, the maximum value of the heat capacity is enhanced below 20 K. These results, as well as the magnetic susceptibility, were analyzed by employing a numerical calculation based on the anisotropic Heisenberg model in one dimension. The analyses revealed that: i the peak in the magnetic-susceptibility data around 25 K is due to an antiferromagnetic short-range order SRO formation associated with d electrons, and ii electrons fall into an antiferromagnetic state below 13 K. The spin-flop field of electrons is approximately 80 kOe at 9K .

Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantumJ1XXZ–J2XXZmodel on the square lattice

We study the zero-temperature phase diagram of the two-dimensional quantum ${J}_{1}^{XXZ}--{J}_{2}^{XXZ}$ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy $\ensuremath{\Delta}$ on the $z$-aligned N\'eel and (collinear) stripe states, as well as on the $xy$-planar-aligned N\'eel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states, on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two quantum triple points (QTPs) at $({\ensuremath{\Delta}}^{c}=\ensuremath{-}0.10\ifmmode\pm\else\textpm\fi{}0.15,\text{ }{J}_{2}^{c}/{J}_{1}=0.505\ifmmode\pm\else\textpm\fi{}0.015)$ and $({\ensuremath{\Delta}}^{c}=2.05\ifmmode\pm\else\textpm\fi{}0.15,\text{ }{J}_{2}^{c}/{J}_{1}=0.530\ifmmode\pm\else\textpm\fi{}0.015)$, between which an intermediate magnetically disordered phase emerges to separate the quasiclassical N\'eel and stripe collinear phases. Above the upper QTP $(\ensuremath{\Delta}\ensuremath{\gtrsim}2.0)$ we find a direct first-order phase transition between the N\'eel and stripe phases, exactly as for the classical case. The $z$-aligned and $xy$-planar-aligned phases meet precisely at $\ensuremath{\Delta}=1$, also as for the classical case. For all values of the anisotropy parameter between those of the two QTPs there exists a narrow range of values of ${J}_{2}/{J}_{1}$, ${\ensuremath{\alpha}}^{{c}_{1}}(\ensuremath{\Delta})l{J}_{2}/{J}_{1}l{\ensuremath{\alpha}}^{{c}_{2}}(\ensuremath{\Delta})$, centered near the point of maximum classical frustration, ${J}_{2}/{J}_{1}=\frac{1}{2}$, for which the intermediate phase exists. This range is widest precisely at the isotropic point, $\ensuremath{\Delta}=1$, where ${\ensuremath{\alpha}}^{{c}_{1}}(1)=0.44\ifmmode\pm\else\textpm\fi{}0.01$ and ${\ensuremath{\alpha}}^{{c}_{2}}(1)=0.59\ifmmode\pm\else\textpm\fi{}0.01$. The two QTPs are characterized by values $\ensuremath{\Delta}={\ensuremath{\Delta}}^{c}$ at which ${\ensuremath{\alpha}}^{{c}_{1}}({\ensuremath{\Delta}}^{c})={\ensuremath{\alpha}}^{{c}_{2}}({\ensuremath{\Delta}}^{c})$.

Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdopedYBa2Cu3O6.45

Using series expansions and spin-wave theory, we calculate the spin-stiffness anisotropy ${\ensuremath{\rho}}_{sx}/{\ensuremath{\rho}}_{sy}$ in Heisenberg models on the square lattice with spatially anisotropic couplings ${J}_{x},{J}_{y}$. We find that for the weakly anisotropic spin-half model $({J}_{x}\ensuremath{\approx}{J}_{y})$, ${\ensuremath{\rho}}_{sx}/{\ensuremath{\rho}}_{sy}$ deviates substantially from the naive estimate ${\ensuremath{\rho}}_{sx}/{\ensuremath{\rho}}_{sy}\ensuremath{\approx}{J}_{x}/{J}_{y}$. We argue that this deviation can be responsible for pinning the electronic liquid crystal direction, an effect recently discovered in YBCO. For completeness, we also study the spin stiffness for arbitrary anisotropy ${J}_{x}/{J}_{y}$ for spin-half and spin-one models. In the limit of ${J}_{y}/{J}_{x}\ensuremath{\rightarrow}0$, when the model reduces to weakly coupled chains, the two show dramatically different behavior. In the spin-one model, the stiffness along the chains goes to zero, implying the onset of Haldane-gap phase, whereas for the spin-half model, the stiffness along the chains increases monotonically from a value of $0.18{J}_{x}$ for ${J}_{y}/{J}_{x}=1$ toward $0.25{J}_{x}$ for ${J}_{y}/{J}_{x}\ensuremath{\rightarrow}0$. In the latter case, spin-wave theory breaks down qualitatively, presumably due to the onset of topological terms with strong anisotropy.

DOUBLE-LAYER THIN FILMS MAGNETIC PROPERTIES DEPENDENCE ON ANISOTROPIC HEISENBERG MODEL PARAMETERS

The study of thin ferromagnetic films has become a field of great interest due to their importance for applications in magnetic-recording media, in order to create ultrahigh density magnetic data storage. Such an interest is also due to numerous specific phenomena related to the low dimension of these systems. In this paper we investigate the magnetic properties of bilayer thin film. The specific behavior of the mentioned system type is simulated using the Monte Carlo technique, in the extended anisotropic Heisenberg model. The magnetization, out-of-plane and in-plane magnetic susceptibilities behaviors according to temperature are investigated in order to find out the contingent magnetic ordering phase and the critical temperature, for two easy-axis anisotropy set parameter assignments. We have also presented the specific heat as a function of temperature for different direct exchange parameter values and we have found out a single-peak shape of the graphs, the critical point traveling to lower temperatures as the direct exchange parameter decreases, the similarity of the two presented cases being evident.

Monte Carlo Study on Induced Antiferromagnetic Phase in Bilayer Films Using Anisotropic Extended Heisenberg Model

In this paper we study the magnetic bearing of a bilayer film in anisotropic extended Heisenberg model, using the Monte Carlo method. In this way, by computing the out-of-plane uniform and staggered magnetization, in-plane uniform magnetization, out-of-plane and in-plane magnetic susceptibility, we point out the existence of an antiferromagnetic phase induced in the superior layer as a consequence of the fixed ferromagnetic arrangement of the spins in the base layer. We can also distinguish the existence of two phase transitions which occur in the physical system: antiferromagnetism → mixed phase transition and antiferromagnetism → XY -like phase transition, corresponding to the two physical parameter settings.

Monte Carlo study on bilayer thin films magnetic properties dependence with discontinouos anisotropy parameters

Abstract In the last few years there has been significant interest in the field of thin films, due to numerous specific phenomena related to the low dimension of these systems, and to the large opportunities in development of high technologies based on their specific magnetic and electronic properties. When dealing with systems of reduced dimensionality it is important to take into account the influence of magnetic anisotropies. In this paper we investigate the magnetic properties of bilayer thin film. This behavior is modeled using Monte Carlo simulations, in the Extended Anisotropic Heisenberg Model. The magnetization, out-of-plane and in-plane magnetic susceptibilities, and also the specific heat bearings according to temperature are investigated in order to find the potential magnetic ordering phases and the critical temperatures, for two sets parameter assignments. For quasi-uniform anisotropy parameters of the film we detect the ferromagnetism-paramagnetism transition and then, by changing the model parameters values, we relieve a short range ferromagnetic ordering phase arising from the antiferromagnetic base layer coupling influence and from easy-plane anisotropy discontinuity on the layers interface.

Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: A renormalization-group approach

Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter Delta (such that Delta=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.

Green function method study of the anisotropic ferromagnetic Heisenberg model on a square lattice

We study the phase diagram of the anisotropic ferromagnetic Heisenberg model on a square lattice. We use the double-time Green’s function method within the Callen decoupling approximation. The dependence of the Curie temperature T c on the spin S and on the anisotropy parameter Δ ( Δ = 0 and 1 correspond to the isotropic Heisenberg and Ising model, respectively) is obtained explicitly. Our results are in agreement with results obtained from other theoretical approaches.

Frequency dispersion of hysteresis in core/shell magnetic nanoparticle: Monte Carlo simulation

Based on the uniaxially anisotropic Heisenberg model, we investigated the frequency dispersion of dynamic hysteresis for an exchange-biased ferromagnetic core/antiferromagnetic shell nanoparticle using Monte Carlo simulation. The frequency dispersion of the dynamic hysteresis shows both the spin-reversal resonance and spin-tilting resonance. The power-law scaling behaviors over both the low-frequency and high-frequency regimes are demonstrated, and it is shown that the exchange coupling on the core/shell interface has no effect on the power-law scaling of the hysteresis dispersion. The dynamic effect of the exchange bias is insignificant either.

Persistent spin waves above the Néel temperature inYMnO3

We have investigated the spin excitations in the frustrated triangular antiferromagnet $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ by inelastic neutron scattering in the ordered magnetic state and also above the N\'eel temperature. In the ordered phase, we observe broad spin excitations, which can be described by an anisotropic Heisenberg model. Above ${T}_{N}$, well defined signatures of persistent spin waves were found evidenced by inelastic peaks in energy spectra. Neatly separated excitations from the quasielastic fluctuations have been identified in this two-dimensional magnetic system. The clear observation might be related to the geometrical frustrated and short ranged ordered nature of this triangular antiferromagnet.

A model for vortex formation in magnetic nanodots

We use Monte Carlo simulation to study the vortex nucleation on magnetic nanodots at low temperature. In our simulations, we have considered a simple microscopic two-dimensional anisotropic Heisenberg model with term to describe the anisotropy due to the presence of the nanodot edge. We have considered the thickness of the edge, which was not considered in previous works, introducing a term that controls the energy associated to the edge. Our results clearly show that the thickness of the edge has a considerable influence in the vortex nucleation on magnetic nanodots. We have obtained the hysteresis curve for several values of the surface anisotropy and skin depth parameter (ξ). The results are in excellent agreement with experimental data.

Entanglement in the 1D extended anisotropic Heisenberg model

We present a study of entanglement in the case of the 1D extended anisotropic Heisenberg model. We investigate two quantum phase transitions (QPTs) within the previously found ergodicity phase diagram [E. Plekhanov, A. Avella, F. Mancini, Phys. Rev. B 74 (2006) 115120]. Our calculations are done by means of the numerically exact Lanczos method at T = 0 , followed by a finite-size scaling. As a measure of entanglement we use the concurrence for two spins out of the system. We conclude from our studies that these QPTs are accompanied by a qualitative entanglement change.

Magnetism and the effect of anisotropy with a one-dimensional monatomic chain of cobaltusing a Monte Carlo simulation

The magnetic properties of a one-dimensional (1D) monatomic chain of Co reported in aprevious experimental work are investigated by a classical Monte Carlo simulation based onthe anisotropic Heisenberg model. In our simulation, the effect of the on-site uniaxial anisotropy,Ku, on each individual Co atom and the nearest neighbour exchange interaction,J, are accounted for. The normalized coercivityHC(T)/HC(TCL) is found to show auniversal behaviour, HC(T)/HC(TCL) = h0(eTB/T−e) inthe temperature interval TCL<T≤TBCal, arising from the thermal activation effect. In the above expression,h0 is aconstant, TBCal is the blocking temperature determined by the calculation, andTCL is the temperature above which the classical Monte Carlo simulation gives a gooddescription of the investigated system. The present simulation has reproducedthe experimental features, including the temperature dependent coercivity,HC(T), and the angular dependence of the remanent magnetization,MR(θ, ϕ), upon the relativeorientation (θ, ϕ) of theapplied field H. In addition, the calculation reveals that the ferromagnetic-likeopen hysteresis loop is a result of a slow dynamical process atT<TBCal. The dependence of thedynamical TBCal on the fieldsweeping rate R, the on-siteanisotropy constant Ku, and the number of atoms in the atomic chain,N, has been investigated in detail.

Spin dynamics ofYMnO3studied via inelastic neutron scattering and the anisotropic Hubbard model

We have investigated the spin dynamics of $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ by inelastic neutron scattering and determined the spin-wave dispersion at low temperature. The spin-wave dispersions at low temperature have been analyzed with a simple nearest-neighbor anisotropic Heisenberg model and also by an anisotropic Hubbard model. Best fits are obtained only in the strong-coupling limit $(U∕t&gt;\ensuremath{\sim}15)$, with planar exchange energy $J=4{t}^{2}∕U\ensuremath{\simeq}2.4\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, and anisotropy terms ${D}_{z}={U}_{{x}^{\ensuremath{'}}}\ensuremath{-}{U}_{{z}^{\ensuremath{'}}}\ensuremath{\simeq}0.32\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and ${D}_{y}={U}_{{x}^{\ensuremath{'}}}\ensuremath{-}{U}_{{y}^{\ensuremath{'}}}\ensuremath{\simeq}0.033\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. We have shown that in the strong-coupling limit, the anisotropic Hubbard model maps into the anisotropic Heisenberg model.

Canonical sequence method applied to a two-dimensional spin system

A number of years ago, Horn and Weinstein introduced a novel nonperturbative method, the t-expansion, for calculating ground-state expectation values for Hamiltonian systems. Recently Samaj et al. have generalized the t-expansion technique and the related connected moments expansion to a more general canonical sequence. In the present work we have expounded upon this work and have applied this to the two-dimensional square anisotropic XXZ Heisenberg model.