On the Spectra of the Kink for Ferromagnetic XXZ Models

We consider the kink (infinite volume nontranslationally invariant ground states) of the ferromagnetic XXZ models on the multi-dimensional lattices. We obtained the following results: (i) The pure states satisfying the local zero energy condition are necessarily product states. (ii) The Hamiltonian in the GNS representation of the kink has no gap between the ground-state eigenvalue and the rest of the spectra.     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e.Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.``     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e. Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.     

On the Spectrum of the XXZ-Chain at Roots of Unity

In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ model at roots of unity, i.e., =(q+q ^–1)/2 with q ^2N =1 for integer N2. They found a certain pattern of degeneracies and linked it to the sl ₂-loop symmetry present in the commensurable spin sector—S ^z 0 modN. We show that the degeneracies are due to an unusual type of zero-energy transparent excitation, the cyclic bound state. The cyclic bound states exist both in the commensurable and in the incommensurable sectors indicating a symmetry group present, of which sl ₂-loop algebra is a partial manifestation. Our approach treats both sectors on even footing and allows us to obtain analytically an explicit expression for the degeneracies in the case N=3.     

Improved Bounds on the Spectral Gap Above Frustration-Free Ground States of Quantum Spin Chains

Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the martingale method. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.     

The Spectral Gap of the 2-D Stochastic Ising Model with Mixed Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an l×l box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length l in the boundary is bounded by l, where <1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on ), the spectral gap decreases exponentially in l.     

The Spectral Gap of the 2-D Stochastic Ising Model with Nearly Single-Spin Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N×N box, with boundary conditions which are plus except for small regions at the corners which are either free or minus. The spectral gap decreases exponentially in the size of the corner regions, when these regions are of size at least of order logN. This means that removing as few as O(logN) plus spins from the corners produces a spectral gap far smaller than the order N ^–2 gap believed to hold under the all-plus boundary condition. Our results are valid at all subcritical temperatures.     

The Spectral Gap for the Kawasaki Dynamics at Low Temperature

In this paper we analyze the convergence to equilibrium of Kawasaki dynamics for the Ising model in the phase coexistence region. First we show, in strict analogy with the nonconservative case, that in any lattice dimension, for any boundary condition and any positive temperature and particle density, the spectral gap in a box of side L does not shrink faster than a negative exponential of the surface L ^d–1. Then we prove that, in two dimensions and for free boundary condition, the spectral gap in a box of side L is smaller than a negative exponential of L provided that the temperature is below the critical one and the particle density satisfies (*_–, *₊), where *_± represents the particle density of the plus and minus phase, respectively.     

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform,classical fluids

Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current interest in this area are briefly discussed.     

Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green＇s function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along Kx direction perpendicular to the superlattice plane. The spin quantum numbers and the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency wg1 in middle of the energy gap Δw12 is complicated, and the frequency wg1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies wg2, wg3, and wg4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbers in each layer are same, the frequencies wg1, wg2, wg3, and wg4 all increase monotonously with increasing interlayer exchange couplings.     

Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green's function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along K_x direction perpendicular to the superlattice plane. The spin quantum numbersand the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency ω_g1 in middle of the energy gap Δω₁₂ is complicated, and the frequency ω_g1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies ω_g2, ω_g3, and ω_g4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbersin each layer are same, the frequencies ω_g1, ω_g2, ω_g3, and ω_g4 all increasemonotonously with increasing interlayer exchange couplings.     

Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder

Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J_×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.     

Symmetry of the pentacene molecule and classification of electron states studied in the frame of group action on a set

Pentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.     

Integrable Deformations of the (2+1)-Dimensional Heisenberg Ferromagnetic Model

Based on the covariant prolongation structure technique,we construct the integrable higher-order deformations of the (2+1)-dimensional Heisenberg ferromagnet model and obtain their su(2)×R(λ) prolongation structures.By associating these deformed multidimensional Heisenberg ferromagnet models with the moving space curve in Euclidean space and using the Hasimoto function,we derive their geometrical equivalent counterparts,i.e.,higher-order (2+1)-dimensional nonlinear Schrödinger equations.     

Spectral Gaps of Quantum Hall Systems with Interactions

A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb–Schultz–Mattis method [Ann. Phys. (N.Y.) 16:407 (1961)]. The model is defined on an infinitely long strip with a fixed, large width, and the Hilbert space is restricted to the lowest (n _max+1) Landau levels with a large integer n _max. We prove that, for a noninteger filling of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also prove the following two theorems: (a) If a pure infinite-volume ground state has a nonzero excitation gap for a noninteger filling , then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a nonzero excitation gap, the filling factor must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions giving the quantized Hall conductance are favored exclusively.     

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.     

阻挫诱导的亚铁磁性Heisenberg系统中的量子相变

利用密度矩阵重整化群(DMRG)方法研究磁性阻挫对一种S=1/2准一维反铁磁自旋链但却具有亚铁磁性的Heisenberg系统基态的影响.计算了单个晶胞的基态能、自旋关联函数以及自旋能隙.研究表明这种Heisenberg自旋系统的基态随着阻挫α的增强将从磁有序相变化到自旋无序相，并且伴随着自旋能隙的出现，量子相变点为α≈0.412.同时线形链上格点间自旋长程关联值的计算结果表明在磁有序区间体系的磁有序性质随着α的增强而减弱，阻挫在0≤α<     

半导体光电探测器响应度测试装置的研制

分析了半导体光电探测器光谱响应度的测试原理;研制了一套波长为０．４～１．１μｍ的光谱响度测试装置。该装置采用双光路替代法,可以测试绝对光谱响应度、相对光谱响应度和量子效率,并可减小光源不稳定性对测试结果的影响,最终给出了测试结果比对。