Scaling near the quantum-critical point in the SO(5) theory of the high-T(c) superconductivity

We study the quantum-critical point scenario within the unified theory of superconductivity and antiferromagnetism based on the SO(5) symmetry. Closed-form expression for the quantum-critical scaling function for the dynamic spin susceptibility is obtained from the lattice SO(5) quantum nonlinear sigma-model in three dimensions, revealing that in the quantum-critical region the frequency scale for spin excitations is simply set by the absolute temperature. Implications for the non-Fermi liquid behavior of the normal-state resistivity due to spin fluctuations in the quantum-critical region are also presented.     

Long-wavelength dynamics of the two-dimensional antiferromagnet

We perform the long-wavelength reduction of the two-dimensional quantum lattice rotator model. An intermediate scale is introduced and the short-wavelength antiferromagnetic spin fluctuations are integrated out. The saddle-point solution for the generalized continuous sigma-model in terms of parameters of the initial model is constructed.     

Spinor dipolar bose-einstein condensates: classical spin approach

Bose-Einstein condensates which are dominated by magnetic dipole-dipole interaction are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from the large spin limit to obtain an effective minimal Hamiltonian. This is a version extended from a nonlinear sigma model. By solving the Gross-Pitaevskii equation, we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.     

Single-Particle Coherence and Spin Squeezing in Four-Qubit Phase State

We investigate single-particle coherence and spin squeezing in four-qubit phase state governed by an one-axis twisting Hamiltonian. In particular, we are interesting in the dependence of single-particle coherence and spin squeezing on the nonlinear interaction. It is shown that single-particle coherence and spin squeezing parameter only depend on the nonlinear interaction and they are periodic function of nonlinear interaction.     

Path Integral for an Effective Two Level Atom in a Kerr-Like Medium and Stark Shift with a Pseudo Hermitian Hamiltonian

We use the coherent state path integral and a angular model for the spin to solve the generalized Jaynes-Cummings model with a pseudo-hermitian Hamiltonian and nonlinear Kerr cavity. The propagators are given explicitly as perturbation series. These are summed up exactly. The energy spectrum and the bi-orthonormal basis of states are deduced.     

Spin response in nonlocal nonlinear optics

A novel effect of the electron spin in nonlinear optics is predicted. Starting from the Pauli Hamiltonian, we present the influence of the electron spin on the nonlinear optical response of a homogeneous electron gas in the low temperature limit. It is shown that the longitudinal second-harmonic response which results from a transverse incoming field differs significantly from the usual paramagnetic response when spin effects are included. The calculation is done both with and without screening.     

Spin-charge separation and the Pauli electron

The separation between the spin and the charge converts the quantum mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian Georgi-Glashow model, which is notorious for its magnetic monopoles and confinement. The independent spin and charge fluctuations both lead to the Faddeev model, suggesting the existence of a deep duality structure and indicating that the fundamental carriers of the spin and charge are knotted solitons. The text was submitted by the authors in English.     

Inelastic neutron scattering study and Hubbard model description of the antiferromagnetic tetrahedral molecule Ni<Subscript>4</Subscript>Mo<Subscript>12</Subscript>

The tetrameric Ni(II) spin cluster Ni₄Mo₁₂ has been studied by INS. The data were analyzed extensively in terms of a very general spin Hamiltonian, which includes antiferromagnetic Heisenberg interactions, biquadratic 2-spin and 3-spin interactions, a single-ion magnetic anisotropy, and Dzyaloshinsky-Moriya interactions. Some of the experimentally observed features in the INS spectra could be reproduced, however, one feature at 1.65 meV resisted all efforts. This supports the conclusion that the spin Hamiltonian approach is not adequate to describe the magnetism in Ni₄Mo₁₂. The isotropic terms in the spin Hamiltonian can be obtained in a strong-coupling expansion of the Hubbard model at half-filling. Therefore detailed theoretical studies of the Hubbard model were undertaken, using analytical as well as numerical techniques. We carefully analyzed its abilities and restrictions in applications to molecular spin clusters. As a main result it was found that the Hubbard model is also unable to appropriately explain the magnetism in Ni₄Mo₁₂. Extensions of the model are also discussed.     

Single-Particle Coherence and Spin Squeezing in Two-Particle Phase State

We investigate the relation between the single-particle coherence and spin squeezing in two-particle phase state governed by an one-axis twisting Hamiltonian. The single-particle coherence and spin squeezing parameter only depends on the nonlinear interaction, and they have the same period of oscillation and the maximum and the minimum.     

Integrable and nonintegrable classical spin clusters

The nonlinear dynamics is investigated for a system ofN classical spins. This represents a Hamiltonian system withN degrees of freedom. According to the Liouville theorem, the complete integrability of such a system requires the existence ofN independent integrals of the motion which are mutually in involution. As a basis for the investigation of regular and chaotic spin motions, we have examined in detail the problem of integrability of a two-spin system. It represents the simplest autonomous spin system for which the integrability problem is nontrivial. We have shown that a pair of spins coupled by an anisotropic exchange interaction represents a completely integrable system for any values of the coupling constants. The second integral of the motion (in addition to the Hamiltonian), which ensures the complete integrability, turns out to be quadratic in the spin variables. If, in addition to the exchange anisotropy also singlesite anisotropy terms are included in the two-spin Hamiltonian, a second integral of the motion quadratic in the spin variables exists and thus guarantees integrability, only if the model constants satisfy a certain condition. Our numerical calculations strongly suggest that the violation of this condition implies not only the nonexistence of a quadratic integral, but the nonexistence of a second independent integral of motion in general. Finally, as an example of a completely integrableN-spin system we present the Kittel-Shore model of uniformly interacting spins, for which we have constructed theN independent integrals in involution as well as the action-angle variables explicitly.     

An integrable 3D model for Heisenberg ferromagnetic spin system with biquadratic interactions

We formulate a model Hamiltonian to a 3D Ferromagnetic spin system incorporating biquadratic interactions. The dynamics is represented by a higher order (3+1) dimensional integrable nonlinear Schrödinger equation. We construct the Lax pair associate with the system and find multisoliton solutions using Darboux transformation(DT). We bilinearize the equation using Hirota’s bilinearization procedure and find one soliton solution.     

Does the XY model have an integrable continuum limit?

The quantum field theory describing the massive O(2) non-linear sigma-model is investigated through two non-perturbative constructions: the form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.     

Continuous weak measurement and nonlinear dynamics in a cold spin ensemble

A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a nonperturbing measurement on the much longer time scale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.     

Magnon squeezing states in a ferromagnet

In this Letter we discuss squeezing state of magnon in ferromagnet, which permits a reduction in the quantum fluctuation of the spin component to below the zero-point quantum noise level of coherent magnon states. We investigate the generation of squeezed magnon state through calculating the expectation values of spin component fluctuation. The mean field theory is introduced in dealing with the nonlinear interaction terms of Hamiltonian of magnon system.     

串型耦合双量子点处于自旋阻塞区时磁输运性质的研究

使用双杂质安德森模型的哈密顿量,从理论上研究了串型耦合双量子点系统处于自旋阻塞区时的磁输运性质,并用主方程近似方法求解了哈密顿量.结果表明,自旋轨道耦合作用导致的双量子点间的自旋反转隧穿能够解除系统的自旋阻塞.同时也研究了超精细相互作用导致的在量子点内自旋反转和双量子点之间的自旋关联对系统的磁输运性质的影响,取得了一些有价值的结果,并对相关的物理问题进行了讨论.     

Squeezing States of Magnons in a Ferromagnet

In this paper, we conduct an investigation into magnon self-squeezing states in a ferromagnet. In these states, the quantum fluctuations of the spin components can be lower than the zero-point quantum fluctuations of the coherent states. Through calculating the expectation values of spin fluctuations we gain the condition of achieving magnon self-squeezing. We introduce the mean-field theory for dealing with the nonlinear interaction term of Hamiltonian of magnon system.     

Effects of the Berry phase and instantons in one-dimensional Kondo-Heisenberg model

Motivated by the global phase diagram of antiferromagnetic heavy-fermion metals, we study the Kondo effect from the perspective of a nonlinear sigma model in the one-dimensional Kondo-Heisenberg model away from half-filling. We focus on the effects of the instanton configurations of the sigma-model field and the associated Berry phase. Guided by the results derived using bosonization methods, we demonstrate that the Kondo-singlet formation is accompanied by an emergent Berry phase. This Berry phase also captures the competition between the Kondo-singlet formation and spin-Peierls correlations. Related effects are likely to be realized in Kondo lattice systems in higher dimensions.     

Derivation of a hydrodynamic equation for Ginzburg-Landau models in an external field

The lattice approximation to a time-dependent Ginzburg-Landau equation is investigated in the presence of a small external field. The evolution law conserves the spin, but is not reversible. A nonlinear diffusion equation of divergence type is obtained in the hydrodynamic limit. The proof extends to certain stochastically perturbed Hamiltonian systems.