Computer Modeling of Phase Transformations and Critical Properties of the Frustrated Heisenberg Model for a Cubic Lattice

Physics of the Solid State - The investigation of the phase transformations and critical properties of the Heisenberg antiferromagnetic model on a cubic lattice was performed by the Monte Carlo...     

Asymptotics of the Mean-Field Heisenberg Model

We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cramér- and Sanov-type large deviations principles for the total spin and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the total spin throughout the phase transition using Stein’s method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.     

Phase Transitions and the Critical Properties of the Heisenberg Model on a Body-Centered Cubic Lattice

Physics of the Solid State - The Monte Carlo replica technique is used to study phase transitions and the thermodynamic and critical properties of the three-dimensional Heisenberg antiferromagnetic...     

On the Generalized Heisenberg Supermagnetic Model

In this paper, we construct the generalized Heisenberg supermagnetic models with two different constraints and investigate the integrability of the super integrable systems. By virtue of the gauge transformation, their corresponding gauge equivalent counterparts are derived, i.e., the super and fermionic mixed derivative nonlinear Schrödinger equations, respectively.     

Solitons in the Two-Dimensional Antiferromagnetic Heisenberg Model

An effective Hamiltonian of the two-dimensional antiferromagnetic Heisenberg model is derived by using the Holstein-Primakoff transformation. Three nonlinear coupled partial equations of motion are obtained. In the long-wavelength approximation, these equations, are reduced to the envelope function equations by the method of multiple scales. The amplitude functions satisfy the nonlinear Schrodinger equation. Introducing an inverse scatteriag transformation, the single-, two- and multi-soliton solutions in the two-dimensional antiferromagnetic Heisenberg model are investigated.     

Photoluminescence of manganese-doped LiNaGe4O9 crystals

The excitation spectra and photoluminescence spectra of manganese-doped LiNaGe₄O₉ crystals have been studied experimentally. It has been shown that the manganese ions provide strong red and weak yellow-green luminescences, whose intensities differently change upon the transition of the crystal from the paraelectric to ferroelectric phase. The possible localization and charge state of the manganese ions in LiNaGe₄O₉ crystals have been discussed.     

Integrable Deformations of Heisenberg Supermagnetic Model

We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/1）×U（1））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.     

The Heisenberg Model of the He Atom Revisited

The present work is devoted to a study of the Heisenberg model of the He atom. We consider the subset of the singlet states, in which one of the electron is kept on its 1s orbital. This spectrum is treated as a pseudo two-body problem. Use is made of a method designed to solve the inverse problem from bound states to determine the local equivalent potential seen by the second electron. The problem is simplified by the use of parametric expressions instead of a full numerical determination of the local equivalent potential. It keeps the numerical effort to a reasonable level. By construction, the local equivalent potential should fit the experimental eigenvalues, which is well achieved with the proposed simplified expressions. It shows the validity of the Heisenberg model for the excited states. It yields also a value for the mean square radius of the He atom. This one is in good qualitative agreement with the value derived from large basis calculations of the He ground state.     

多量子位Heisenberg模型中纠缠的时间演化特性

研究了多量子位Heisenberg模型中纠缠的时间演化特性, 并给出了平均纠缠度〈C〉和多体纠缠度Q的解析表达式. 结果发现无论是对〈C〉还是对Q随着时间t的不断增长, 它们均先线性的增大, 而后达到一近似稳定状态, 并绕一平衡值做无规则的上下震荡. 若进一步考察N〈C〉则还可以发现, 纠缠上下震荡的平衡值与Heisenberg链的长度几乎无关, 而仅由它们的次近邻耦合常数J决定.     

Slave-Fermion Mean-Field Theory of Heisenberg Model

A nearly half-filled two-dimensional Heisenberg model is investigated. A slave-fermion method with fermions as the charge carriers and bosons as the spin carriers is proposed. The ground state shows antiferromagnetic long range order at T = 0. The spin-spin correlation and static susceptibility are also obtained.     

Slave-Fermion Mean-Field Theory of Heisenberg Model

A nearly half-filled two-dimensional Heisenberg model is investigated. A slave-fermion method with fermions as the charge carriers and bosons as the spin carriers is proposed. The ground state shows antiferromagnetic long range order at T = 0. The spin-spin correlation and static susceptibility are also obtained.     

The 2-dimensional O(4) symmetric Heisenberg ferromagnet in terms of rotation-invariant variables

After the introduction of rotation-invariant auxiliary variables, the integration over all rotation-variant variables (spins) in the O(4) symmetric two-dimensional Heisenberg ferromagnet can be performed. The resulting new hamiltonian involves a sum over closed loops. It is complex and invariant under U(1) gauge transformations. Rühl's boson representation is used to derive the result.     

海森堡模型中量子隐形传递的研究

通过对海森堡模型中量子热纠缠的研究,进而研究以海森堡热纠缠混合态为信道的量子隐形传递,计算出纠缠度和保真度,分析外界环境(温度、磁场等)对热纠缠及隐形传递的影响.