Heisenberg Spin Model Research Articles

Theoretical studies of d– d magnetic interaction in organic superconductors

In the κ-(BETS) 2FeCl 4 crystal as one of organic magnetic-metal crystals, localized spins of d-orbitals in FeCl 4 - anions is expected to play an important role to magnetic properties. To investigate all the magnetic interactions between neighboring two FeCl 4 - anions, various spatial conformation of dimers were assumed and studied. For variety of configurations of FeCl 4 - anion dimers, the values of effective exchange integral ( J) in the Heisenberg spin model were calculated by using ab initio MO methods. It was found that very weak ferromagnetic interaction existed in a certain conformation, though antiferromagnetic interaction was reproduced in most of all conformations.

Theoretical Calculations of Magnetic Interactions in Frustrated Antiferromagnetic Cluster

Inter-dimer magnetic interactions (Jab(D) ) between (BEDT-TTF)2 +• dimers in the κ-(BEDT-TTF)2Cu2(CN)3 crystal has been studied theoretically. In these crystals, triangular lattice structure with spin frustration has been discovered and experimental studies have been performed by several research groups. We have calculated the inter-dimer Jab(D) values by using several methods. In addition, we have analyzed the spin lattice with optimization of θ angle in classical Heisenberg spin model and with numerical diagonalization in quantum Heisenberg spin model.

Crystal structure and magnetic properties of the coupled spin dimer compound SrCu 2(TeO 3) 2Cl 2

Single crystals of the strontium copper tellurium oxochloride SrCu 2(TeO 3) 2Cl 2 were synthesized via solid-gas reactions in sealed evacuated silica tubes. The compound crystallizes in the monoclinic system, space group P2 1, a=7.215(2), b=7.2759(15), c=8.239(2) Å, β=96.56(4)°, Z=2. The building units are [SrO 6Cl 2] irregular polyhedra, [CuO 4] and [CuO 3Cl] square planes, [TeO 3E] tetrahedra and [TeO 3+1E] trigonal bipyramids; E being the 5 s 2 lone pair of Te(IV). The Cu atoms can be regarded as forming a chain of weakly connected dimers. The magnetic susceptibility of the compound shows a broad maximum typical for antiferromagnetic spin fluctuations with a non-magnetic ground state. A Heisenberg spin model with coupled s=1/2 dimers leads to a satisfactory fitting of the experimental data.

Finite quantum Heisenberg spin models and their approach to the classical limit

We determine the temperature range over which classical Heisenberg spin models closely reproduce the zero-field susceptibility of the corresponding quantum Heisenberg models for a finite number $N$ of interacting quantum spins $s$. Using mostly quantum and classical Monte Carlo methods, as well as analytical methods where applicable, we have explored a variety of geometries, including polygons, open chains, and all Platonic and several Archimedean polytopes. These systems range in size from $N=2$ to 120, and we have considered values of $s$ from $1∕2$ to 50 for both antiferromagnetic and ferromagnetic exchange. Particular attention is devoted to quantifying the slow convergence of the large $s$ quantum data to the limiting classical data. This is motivated by the desire to define conditions where classical Monte Carlo methods can provide useful predictions for finite quantum Heisenberg spin systems.

Phase diagram and critical properties of the spin-1 Heisenberg model with single-ion anisotropy

Abstract We study the spin-1 bilinear-biquadratic Heisenberg model with the single-ion anisotropic term H = J ∑ 〈 i j 〉 [ cos θ S i ⋅ S j + sin θ ( S i ⋅ S j ) 2 ] + D ∑ i ( S i z ) 2 to show that the phase transition and critical behaviors from the large- D phase to other phases in two and three dimensions. The phase boundary of the spin-1 Heisenberg model with biquadratic exchange and single-ion anisotropy D is presented. When the bilinear coupling is antiferromagnetic, it shows that a positive biquadratic coupling constant tends to collaborate with the bilinear term to break the large- D phase while a negative one has the opposite contribution. For the case of θ = π / 4 , all spins occupy the state of | s z = 0 〉 and a second-order phase transition occurs at this point when the system is in the large- D phase.

Spin-liquid phase in an anisotropic triangular-lattice Heisenberg model: Exact diagonalization and density-matrix renormalization group calculations

Based on exact diagonalization and density matrix renormalization group (DMRG) method, we show that an anisotropic triangle lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an exponentially-decaying spin correlator along the weaker coupling direction and a quasi-one-dimensional spin structure factor along the chain direction, in agreement with experiments on the Cs2CuCl4 compounds. In the obtained phase diagram, the spin liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio J'/J=0.78, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime.

Phase diagram and tricritical behavior of the spin-1 Heisenberg model with Dzyaloshinskii–Moriya interactions

Using the two-spin cluster mean-field method, the spin-1 Heisenberg model with Dzyaloshinskii–Moriya (DM) interactions is studied for the simple cubic lattice. For the case of the DM vector coupling D ⇒ = D z ^ ( D is the DM interaction parameter and z ^ is the unit vector of the z-axis direction), the phase diagram of this system and the thermal behavior of the magnetization are obtained, and it is found that the system exhibits the tricritical point. The critical behavior of the system may be interpreted as a result of a competition between the exchange interaction and the DM interaction.

Quantum phase transition of entanglement in Heisenberg spin model with quantized field

In this paper, we investigate the entanglement of a two-spin system with Heisenberg exchange interaction in a quantized field. The pairwise entanglement between bipartite subsystems is obtained. It is shown that the entanglement exhibits a quantum phase transition due to the variation of exchang coupling. Phase diagrams are obtained explicitly. The analogy of the quantum phase transition compared to the case under a classical field are addressed.

Numerical study of magnetic field induced ordering inBaCuSi2O6and related systems

Thermodynamics of spin dimer system $\mathrm{Ba}\mathrm{Cu}{\mathrm{Si}}_{2}{\mathrm{O}}_{6}$ is studied using a quantum Monte Carlo calculation (QMC) and a bond-operator mean field theory. We propose that a new type of boson, which, rather than being hard core, allows up to two occupancies at each site, is responsible for the Bose-Einstein condensation of field induced ordering. Its superfluid density is identified as the square of the in-plane staggered magnetization ${m}_{xy}$ in the ordered phase. We also compare our QMC result of the spin Heisenberg model to those predicted by the mean field theory as well as by the simple hard-core boson model for both large and small intradimer coupling $J$. The asymmetry of the phase diagram of ${m}_{xy}(h)$ of small coupling $J$ in related systems such as $\mathrm{Ni}{\mathrm{Cl}}_{2}\text{\ensuremath{-}}4\mathrm{S}\mathrm{C}(\mathrm{N}{\mathrm{H}}_{2})$ is explained with our new boson operator.

ON THE RELATIONSHIP BETWEEN SIGMA MODELS AND SPIN CHAINS

We consider the two-dimensional O (3) non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl. Phys. B336, 457 (1990)], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient θ of the topological term is quantized as θ=2πs, with s integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-s Heisenberg model. We generalize the analysis to sigma models with other symmetries.

Thermal conductivity of a classical one-dimensional Heisenberg spin model

We investigate the thermal conductivity of classical spin chains through a Green-Kubo approach using both Monte Carlo and Langevin simulations as well as by direct numerical determination of the microscopic heat transfer processes. All three approaches show that magnetic heat conductivity is normal for all finite temperatures and magnetic fields. In ferromagnets, heat conduction grows linearly with the magnetic field while in antiferromagnets this holds only at high fields. At low fields a quadratic decrease leading to a minimum is attributed to spin mode velocity suppression.

Quantum phase transitions in the Fermi–Bose Hubbard model

We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram.

Many-polaron effects in the Holstein model

We derive an effective polaronic interaction Hamiltonian, {\it exact to second order in perturbation}, for the spinless one-dimensional Holstein model. The small parameter is given by the ratio of the hopping term ($t$) to the polaronic energy ($g^2 \omega_0$) in all the region of validity for our perturbation; however, the exception being the regime of extreme anti-adiabaticity ($t/\omega_0 \le 0.1$) and small electron-phonon coupling ($g < 1$) where the small parameter is $t/\omega_0$. We map our polaronic Hamiltonian onto a next-to-nearest-neighbor interaction anisotropic Heisenberg spin model. By studying the mass gap and the power-law exponent of the spin-spin correlation function for our Heisenberg spin model, we analyze the Luttinger liquid to charge-density-wave transition at half-filling in the effective polaronic Hamiltonian. We calculate the structure factor at all fillings and find that the spin-spin correlation length decreases as one deviates from half-filling. We also extend our derivation of polaronic Hamiltonian to $d$-dimensions.

Vacancy effects in an easy-plane Heisenberg model: Reduction ofTcand doubly charged vortices

Magnetic vortices in thermal equilibrium in two-dimensional magnets are studied here in the presence of a low concentration of nonmagnetic impurities (spin vacancies). A nearest-neighbor Heisenberg (XXZ) spin model with easy-plane exchange anisotropy is used to determine static thermodynamic properties and vortex densities via combined cluster and over-relaxation Monte Carlo simulations. Especially at low temperatures, a large fraction of the thermally generated vortices nucleate centered on vacancies, where they have a lower energy of formation. This fact is responsible for the reduction of the vortex-unbinding transition temperature with increasing vacancy concentration, similar to that seen in the planar rotator model. Spin vacancies also present the possibility of the appearance of vortices with double topological charges ($\ifmmode\pm\else\textpm\fi{}4\ensuremath{\pi}$ change in in-plane spin angle), stable only when centered on vacancies.

Current carrying ground state in a bilayer model of strongly correlated systems

Strongly interacting systems have been conjectured to spontaneously develop current carrying ground states under certain conditions. We conclusively demonstrate the existence of a commensurate staggered interlayer current phase in a bi-layer model by using the recently discovered quantum Monte-Carlo algorithm without the sign problem. A pseudospin SU(2) algebra and the corresponding anisotropic spin-1 Heisenberg model are constructed to show the competition among the staggered interlayer current, rung singlet and charge density wave phases.

Auxiliary-fermion approach to critical fluctuations in the two-dimensional quantum antiferromagnetic Heisenberg model

The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Q=1 on each lattice site, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T. This drawback, which is caused by overdamping, is overcome in a `minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths and in the short-range-order regime. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.

Electronic structure and exchange interactions inBaVS3

The electronic structure and spin exchange interactions of a quasi-one-dimensional sulfide ${\mathrm{BaVS}}_{3}$ have been studied within the density functional theory $(\mathrm{DFT})$ with the generalized gradient approximation $(\mathrm{GGA})$ using the projected augmented wave $(\mathrm{PAW})$ method. The on-site Coulomb repulsion has also been taken into account in the $\mathrm{GGA}+U$ approach to unravel the correlation effects on the electronic structure. We found that in the high-temperature hexagonal structure the partially filled ${t}_{2g}$ conduction bands including the broad $d(3{z}^{2}\ensuremath{-}{r}^{2})$ and two narrow $e({t}_{2g})$ orbitals contribute to the conductivity of ${\mathrm{BaVS}}_{3}$, suggesting a weak anisotropy in the electronic transport. Furthermore, our $\mathrm{GGA}+U$ band structure calculations predict an insulating ground state with a narrow gap of $0.15\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${\mathrm{BaVS}}_{3}$ in the low-temperature $(60\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ orthorhombic structure, thereby indicating the Mott-Hubbard mechanism for the low-temperature insulating behavior. Our total energy analyses of the ground-state spin configuration in the low-temperature phases show that the magnetic structure with an intrachain ferromagnetic spin arrangement and an interchain antiferromagnetic spin arrangement that is consistent with a superexchange mechanism through sulfur $3\phantom{\rule{0.3em}{0ex}}p$ orbitals is preferred. We have also estimated the values of exchange integrals by mapping the calculated total energies onto the Heisenberg spin model. It is found that the stronger exchange interaction is ferromagnetic intrachain coupling, while the weaker antiferromagnetic interchain coupling occurs along the $a$ axis. A substantial magnetic anisotropy is found and results in the observed quasi-1D magnetic character in ${\mathrm{BaVS}}_{3}$. This suggests the separation of the spin and charge degrees of freedom as a possible cause of the anomalous properties, e.g., the 3D electronic transport and the quasi-1D magnetism of ${\mathrm{BaVS}}_{3}$.

From the quantum Jacobi–Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one-dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi?Trudi and Giambelli formula (Bazhanov?Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.

Control of the Evolution of Heisenberg Spin Systems

In this paper, we give an algorithm for the control of the unitary evolution operator for the system of two spin 1 2 ’s interacting through Heisenberg interaction. This algorithm allows for arbitrarily bounded control. The results extend previous ones that only concerned the control of a pure state. A Lie group decomposition technique is used to this goal and the problem is reduced to a two level problem with constraints. We also show how the control result allows to obtain information on the initial state through a series of evolutions and measurements. The study of the Heisenberg spin model is motivated by applications in electron paramagnetic resonance and in molecular magnetism. For these systems, the drift which models the interaction between the spins is typically large and cannot be neglected in the control design but it has to be used to reach the objective.