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Existence of Néel order in the S=1 bilinear biquadratic Heisenberg model via random loops

Existence of Néel order in the S=1 bilinear biquadratic Heisenberg model via random loops

1.1. Historical setting. In this work properties of the spin-1 Heisenberg model are de- duced using a random loop model first introduced in the work of Nachtergaele [18]. Random loop models have been around since the work of Tóth [21] and Aizenman and Nachtergaele [1]. In [21] a lower bound was obtained on the pressure of the spin- 1 2 Heisenberg ferromagnet; this improved the bound of Conlon and Solovej [5]. Sharp bounds have recently been found [6]. The loop model presented in [1] applies to the spin- 1 2 Heisenberg antiferromagnet. Both spin models can be applied to higher spins; for a review of these models we refer, for example, to [14]. The work of Ueltschi [23] combined and extended these loop models. It has recently seen attention for its use- fulness in several aspects of quantum spin systems. In [23]; it is shown that there is long-range order in various spin systems, including nematic order in the spin-1 system. The work of Crawford, Ng and Starr [7] on emptiness formation also makes use of the model, as does the work of Björnberg and Ueltschi [4] on decay of correlations in the presence of a transverse magnetic field. The loop model presented here comes from [18]; it is similar in flavour to the Aizenman-Nachtergaele-Tóth-Ueltschi representation. See Refs. [1,18,19,21,23] and references therein.
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An Improved Finite Temperature Lanczos Method and Its Application to the Spin 1/2 Heisenberg Model on the Kagome Lattice

An Improved Finite Temperature Lanczos Method and Its Application to the Spin 1/2 Heisenberg Model on the Kagome Lattice

Another improvement was to employ the effective sampling method for selecting a random vector. Using this sampling we can improve the efficiency of calculations. By the tFTLM, we calculated the specific heat of the spin-1/2 Heisenberg model on the kagome lattice of 30 sites. Our results confirmed the little dependence of the specific heat on the cluster size at T > 0.25 . At 0.15 < < T 0.25 the dependence on the cluster size was small, so that we concluded that the curve of the specific heat changed from the curve at the higher temperature. Also our calculation suggested that the shoulder of the curve survived at the large cluster size at 0.04 < < T 0.3 . Summarizing this work, we proposed the tFTLM that was quite effective for numerical study at extremely low temperature and we presented definite results about the specific heat of the Heisenberg model on the L = 30 kagome lattice.
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A Quantum Dynamics of Heisenberg Model of the Neutron Associated with Beta Decay

A Quantum Dynamics of Heisenberg Model of the Neutron Associated with Beta Decay

In this work we re-examine a model of the nucleons that involve the weak in- teraction which was once considered by Heisenberg; that is a neutron may have the structure of a dwarf hydrogen-like atom. We formulate a quantum dynamics for the Heisenberg model of the neutron associated with interac- tion that involves the beta decay in terms of a mixed Coulomb-Yukawa po- tential and the More General Exponential Screened Coulomb Potential (MGESCP), which has been studied and applied to various fields of physics. We show that all the components that form the MGESCP potential can be derived from a general system of linear first order partial differential equa- tions similar to Dirac relativistic equation in quantum mechanics. There are many interesting features that emerge from the MGESCP potential, such as the MGESCP potential can be reduced to the potential that has been pro- posed to describe the interaction between the quarks for strong force in parti- cle physics, and the energy spectrum of the bound states of the dwarf hydro- gen-like atom is continuous with respect to distance. This result leads to an unexpected implication that a proton and an electron may also interact strongly at short distances. We also show that the Yukawa potential when re- strained can generate and determine the mathematical structures of funda- mental particles associated with the strong and weak fields.
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Beyond the Heisenberg model: Anisotropic exchange interaction between a Cu tetraazaporphyrin monolayer and Fe3O4(100)

Beyond the Heisenberg model: Anisotropic exchange interaction between a Cu tetraazaporphyrin monolayer and Fe3O4(100)

In summary, we demonstrate a strongly anisotropic ex- change coupling possibly augmented by a dipolar compo- nent between the single unpaired spin of the central Cu(II) ion of a porphyrin molecule and the magnetite(100) surface. We propose that the anisotropic coupling results from the competition between ferromagnetic superex- change along Fe-N-Cu [14] and antiferromagnetic super- exchange along Fe-O-Cu [11] with strength modified by the strong spin-orbit coupling [1]. The present experiment on a strongly heterogeneous system was designed to dis- entangle the anisotropic exchange coupling from crystal- line magnetic anisotropy due to anisotropic bonding structures. Nevertheless, our results suggest that aniso- tropic exchange coupling may play an important role in many molecular magnetic systems, although it will often show up as an anisotropic magnetization behavior in homogeneous materials. For a dominant anisotropic cou- pling strength, the conventional Heisenberg model, usually used to describe exchange interaction in molecular mag- nets, becomes inapplicable. The interplay of the exchange interaction with the magnetization direction opens a new pathway to control the spin configuration in single molecu- lar magnets.
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Structure of Essential Spectrum and Discrete Spectrum of the Energy Operator of Three Magnon Systems in the Isotropic Ferromagnetic Non Heisenberg Model with Spin One and Nearest Neighbor Interactions

Structure of Essential Spectrum and Discrete Spectrum of the Energy Operator of Three Magnon Systems in the Isotropic Ferromagnetic Non Heisenberg Model with Spin One and Nearest Neighbor Interactions

We consider a three-magnon system in the isotropic ferromagnetic Non- Heisenberg model with spin one and with a coupling between near- est-neighbors. The structure of essential spectrum and discrete spectrum of the systems in a ν -dimensional lattice are investigated. We obtain the lower and upper estimates for the number of three-magnon bound states of the sys- tem.

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Incorporation of density-matrix wave functions in Monte Carlo simulations: Application to the frustrated Heisenberg model

Incorporation of density-matrix wave functions in Monte Carlo simulations: Application to the frustrated Heisenberg model

first investigate the two–dimensional frustrated Heisenberg model by constructing the DMRG wave function of the ground state for long strips up to a width of eight sites. The ground-state energy and the spin stiffness which are calcu- lated confirm the overal picture described above, but the re- sults are not accurate enough to allow for a conclusive ex- trapolation to larger systems. Then we study an open 10 ⫻ 10 lattice by means of the GFMC technique using DMRG wave functions as the guiding wave function for the impor- tance sampling. The GFMC simulations are supplemented by stochastic reconfiguration as proposed by Sorella 3 as an ex- tension of the fixed node technique. 12 This method avoids the minus sign problem by replacing the walkers regularly by a new set of positive sign with the same statistical properties. The first observation is that GFMC improves the energy of the DMRG technique in a substantial and systematic way as can be tested in the unfrustrated model where sufficient in- formation is available from different sources. Second, the spin correlations become more accurate and less dependent on the technique used for constructing the DMRG wave function. The DMRG technique is focused on the energy of the system and less on the correlations. The GFMC tech- nique probes mostly local correlations of the system as all moves are small and correspond to local changes of the con- figurations. With these spin correlations we investigate the phase diagram for various values of the frustration ratio J 2 /J 1 .
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Entanglement in the Quantum Phase Transition of the Half Integer Spin One Dimensional Heisenberg Model

Entanglement in the Quantum Phase Transition of the Half Integer Spin One Dimensional Heisenberg Model

Heisenberg chains. Our calculations show that the entanglement is maximum in the point ∆ = 1 and the entan- glement is minimum when ∆ = − 1 . Consequently there is a large influence of the quantum critical region on the entanglement. The influence of the quantum phase transition obtained for this system is large as obtained in Reference [1] for the extended Hubbard model for a finite number of particles N.

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Nonperturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model

Nonperturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model

Although RG methods have been successfully applied to a variety of physical problems, the construction of RGT’s ap- plicable to strong-coupling regimes is, apart from a few ex- ceptions, an unsolved and challenging problem. Examples of current research are the strong-coupling quantum spin chains, including the Heisenberg models, 3,4 and nonlinear partial differential equations 共 PDE’s 兲 . 5,6 Standard approaches like perturbation theory in combination with Fourier space RG methods cannot be applied.

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AB INITIO STUDY OF THE POSSIBLE SINGLE-CENTER UNITS FOR BINUCLEAR IRON COMPLEX [Fe2(bpym)3Cl4]

AB INITIO STUDY OF THE POSSIBLE SINGLE-CENTER UNITS FOR BINUCLEAR IRON COMPLEX [Fe2(bpym)3Cl4]

The results obtained show that values of the localized spins on centers in Fe 2 (bpym) 3 Cl 4 complex cannot be presupposed to be equal to 2. The both studied single-center units were shown to have singlet ground states in accordance with experimental data and cannot be used in Heisenberg model. This means, that the only way to successfully develop any suitable model that will describe not only the behavior of the complete system, but the internal interactions that take place there, is to proceed with the magnetic properties of polynuclear complexes quantitatively by both the experimental or theoretical ab initio mean.
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Heisenberg spin triangles in {V6} type magnetic molecules: Experiment and theory

Heisenberg spin triangles in {V6} type magnetic molecules: Experiment and theory

We report the results of systematic experimental and theoretical studies of two closely related species of magnetic molecules of the type {V6}, where each molecule includes a pair of triangles of exchange-coupled vanadyl (VO2+,spin s=1/2) ions. The experimental studies include the temperature dependence of the low- field susceptibility from room temperature down to 2 K, the dependence of the magnetization on magnetic field up to 60 T for several low temperatures, the temperature dependence of the magnetic contribution to the specific heat, and the 1H and 23Nanuclear magnetic resonance spin-lattice relaxation rates 1/T1. This body of experimental data is accurately reproduced for both compounds by a Heisenberg model for two identical uncoupled triangles of spins; in each triangle, the spins interact via isotropic antiferromagnetic exchange, where two of the three V-V interactions have exchange constants that are equal and an order of magnitude larger than the third; the ground-state eigenfunction has total spin quantum number S=1/2 for magnetic fields below a predicted critical field Hc≈74T and S=3/2 for fields above Hc.
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Exchange anisotropy and the dynamic phase transition in thin ferromagnetic Heisenberg films

Exchange anisotropy and the dynamic phase transition in thin ferromagnetic Heisenberg films

A recent study 关 21 兴 of the kinetic spherical model in an oscillatory magnetic field has shown that the oscillation of the system magnetization will always be centered on zero. This implies that the kinetic spherical model cannot support a dynamically ordered phase and so cannot have a DPT. This should also be true for the isotropic Heisenberg model. So in order to exhibit both dynamically ordered and dynamically disordered phases with an associated DPT, the Heisenberg model must be subject to a uniaxial anisotropy. Our work shows that in a thin film where competing surface fields ensure that magnetization reversal proceeds by domain wall motion, there is a critical value for the bilinear exchange anisotropy ⌳ below which there will be no DPT. Further- more, this critical value is a function of the temperature and the strength of the oscillatory field.
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AB INITIO ANALYSIS OF EXCHANGE INTERACTIONS IN [V2O(BIPY)4CL2]2+ COMPLEX

AB INITIO ANALYSIS OF EXCHANGE INTERACTIONS IN [V2O(BIPY)4CL2]2+ COMPLEX

of binuclear systems. ROHF+CI calculation give the order of states with different spin values (Fig. 5) similar to the Heisenberg model (Fig. 5 inserted picture) and even the energy differences between fi rst excited and ground states and second excited and fi rst excited states ratio 4:2 is preserved (according to Lande rule). When carrying out calculations using UHF method it was obtained that ground state is a state with S=2 too but the other UHF calculations results does not coincide with ROHF calculations and Heisenberg model.

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Ab initio study on the magnetostructural properties of MnAs

Ab initio study on the magnetostructural properties of MnAs

First a review of the experimental properties of MnAs is presented and a brief description of the existing phenomeno- logical models is given. Then the results of our ab initio calculations are presented and compared to experiments and models. Within the scope of a Heisenberg model the ex- change coupling constants are calculated for different dis- torted unit cells, and the Curie temperature and its depen- dence on the lattice parameters are evaluated in the mean- field approximation. We also predict the ground-state volume and lattice structure for the paramagnetic state, demonstrat- ing that the phase transitions of MnAs can indeed be ex- plained by ab initio calculations. Finally a simple model for the susceptibility as function of temperature is given and a qualitative description of the phase diagram of MnAs will emerge.
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Violation of Cluster Property in Heisenberg Antiferromagnet

Violation of Cluster Property in Heisenberg Antiferromagnet

In this paper, we investigate the violation of cluster property for Heisenberg quantum spin on the square lattice, whose continuous symmetry is SU(2). SSB in this system can be explained by the effective model which realizes the magneti- zation of the sub-lattices [26]. By this model, we can present a definite descrip- tion of the quasi-degenerate states. Here we should note that the quasi-degenerate states are the essential ingredients of SSB, as stressed in the previous work [25].

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Information Interpretation of Heisenberg Uncertainty Relation

Information Interpretation of Heisenberg Uncertainty Relation

Heisenberg uncertainty relation is one of the fundamental principles of Quan- tum Mechanics. On the other hand, an information approach to Quantum Me- chanics is popular now (for example, see [1] [2] [3]). In this paper, firstly, we consider the classical N -slit interference experiment and calculate the Shannon information entropy for it. This allows obtaining a formulation of the informa- tion interpretation of the uncertainty relation. Then, it is used for an explanation of the entangled photons diffraction picture compression.

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Generalized analogs of the Heisenberg uncertainty inequality

Generalized analogs of the Heisenberg uncertainty inequality

the next section, a generalized analog of the Heisenberg uncertainty inequality for the Eu- clidean motion group M(n) is proved. The last section deals with a generalized analog of the Heisenberg uncertainty inequality for several general classes of nilpotent Lie groups for which the Hilbert-Schmidt norm of the group Fourier transform π ξ (f ) of f attains a

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A NOTE ON BENEDICKS’ THEOREM ON HEISENBERG GROUP

A NOTE ON BENEDICKS’ THEOREM ON HEISENBERG GROUP

In this article, we will prove a stronger result for certain class of functions. We will prove that if a function f defined on the Heisenberg group is supported in a ‘thin set at infinity’ and the group Fourier transform f  () is a rank one operator for each 0, then the function f is the zero function. This ‘thin set at infinity’ includs the compact set as well as the sets of finite Lebesgue measure.

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Hypercomplex Representations of the Heisenberg Group and Mechanics

Hypercomplex Representations of the Heisenberg Group and Mechanics

In this paper we derive mathematical models for various physical setup from hypercomplex representations of the Heisenberg group. There are roots for such hypercomplex characters in the structure of ladder operators associated to three non-isomorphic quadratic Hamiltonians [52, 53]. Such hypercomplex represent- ations may be also useful for many other groups as well, see the example of the SL 2 ( R ) group in [47]. Moreover non-trivial parabolic characters described

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Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions

Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions

mark that, in order to obtain an analytical expression for even larger interaction ranges, one should take into account further terms in the approximation above Eq. (C5), which may be- come relevant for sufficiently-small detunings. In any case, such small MS detunings compromise the validity of a pure effective spin model, as errors due to a thermal phonon popu- lation start playing a dangerous role 10 .

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