梯形自旋链的一种规范场论的形式

考虑无质量费米场和规范场的Pauli相互作用项的系统,在这一理论中耦合常数为无量纲量.该模型等价于自旋1/2反铁磁XXZ量子链.如在模型中引入费米场的味自由度,则可定性描述二条自旋链的梯形结构系统.在这一系统中不再存在无能隙激发. 关键词： 梯形结构 规范场 自旋链     

具有次近邻相互作用的五量子比特XXZ海森伯自旋链的热纠缠

研究具有次近邻相互作用五量子比特XXZ海森伯自旋链在磁场作用下的热纠缠性质,利用数值计算求出最近邻两量子比特和次近邻两量子比特的共生纠缠度(concurrence),分别记为C_(12)和C_(13).研究结果表明,阻挫参数对配对热纠缠具有重要影响,而且阻挫参数的变化对C_(12)和C_(13)的影响也各不相同;温度、磁场、Dzyaloshinkii-Moriya相互作用以及各向异性参数对配对热纠缠有着不同程度的影响;通过选择适当的模型参数,可以有效地调节和提高五量子比特XXZ海森伯自旋链的配对热纠缠.     

具有Dzyaloshinskii-Moriya相互作用的四量子比特海森堡XXZ模型中的热纠缠

研究四量子比特海森堡XXZ模型中配对纠缠的性质,在该系统中引入了Dzyaloshinskii-Moriya (DM)相互作用,通过求解配对纠缠度来讨论最近邻和次近邻两量子比特之间的热纠缠性质. 研究结果表明:对于铁磁和反铁磁两种情形而言,次近邻两量子比特之间不存在配对热纠缠;但在最近邻两量子比特情况时,DM相互作用和各向异性参数Δ对配对热纠缠和临界温度T_c都具有重要的影响,且随着温度T的增加,配对纠缠度逐渐减小直至消失. 因此,选择和调整合适的DM相互作用和各向异性参数,可以有效地控制和提高配对热纠缠. 关键词： 配对纠缠 XXZ模型')" href="#">XXZ模型 Dzyaloshinskii-Moriya相互作用     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

杨-巴克斯特自旋1/2链模型的量子关联研究

量子系统各部分间的量子关联可以作为量子信息应用研究的基础资源. 而量子失协是度量量子关联大小的物理量. 由此研究杨-巴克斯特自旋1/2链模型的量子关联情况. 首先利用两个杨-巴克斯特方程的解得到相应的杨-巴克斯特自旋1/2链模型. 然后, 计算分析热平衡时杨-巴克斯特自旋1/2链模型的量子失协、几何量子失协和量子纠缠随着温度和外磁场的变化情况. 结果表明对于杨-巴克斯特自旋1/2链模型, 量子失协和几何量子失协能够比量子纠缠更好地度量量子关联.     

应用保真度研究两腿XXZ梯子系统的量子相变

本文基于投影纠缠对态的自旋梯子系统的张量网络算法提供了一个有效的方法,来研究两腿自旋1/2的XXZ梯子量子系统的量子临界性,通过与单位格点基态保真度相结合,得到清晰的基态保真度三维图,来探测量子多体系统的量子相变,从而可以绘制出两腿自旋1/2XXZ梯子量子模型的基态相图,在相图中出现铁磁(FM)相、条纹铁磁(SF)相、Néel(N)相、条纹Néel(SN)相、Rung singlet(RS)相、Haldane(H)相、Rung triplet(RT)相、临界XY相(XY1相和XY2相)。在不知道系统是否存在局域序参量或非局域序参量的情况下,可以通过系统的基态波函数,在对称性破缺相中由约化密度矩阵得到局域序参量;或者在对称性相中,找出系统存在的非局域序参量,来完整地描述系统的量子相变和量子临界现象。     

带有三体相互作用的XXZ自旋链模型的隐形传态

本文对基于海森堡XXZ自旋链模型的隐形传态的平均保真度进行了详细计算和分析.通过比较不带三体相互作用、仅带一种三体相互作用和同时带两种三体相互作用的各种海森堡铁磁质和反铁磁质XXZ模型在外磁场正向和反向时的保真度与外磁场和温度的关系,找到了一些理想模型,用这些模型进行隐形传态时需要的外界磁场相对较弱、温度相对较高,这个结论为实验上用海森堡XXZ模型进行隐形传态提供了很好的理论依据.     

具有三体相互作用自旋链的量子相干与量子纠缠

本文研究了具有两种三体相互作用的海森堡XXZ自旋链的量子相干与量子纠缠的特性。研究发现，量子相干性不会出现突然死亡现象且非零量子相干性存在的温度范围大于量子纠缠存在的温度范围，说明量子相干性相对于量子纠缠，具有更强的鲁棒性。在量子临界环境中，量子相干性可以表征本模型的量子相变现象。在铁磁情形中，无论外磁场是否为0，单独调控XZX+YZY三体相互作用对于减缓量子相干性的衰减速率与增大量子相干性存在的温度范围效果最好。在反铁磁情形中，外磁场为0时，XZX+YZY与XZY-YZX两种三体相互作用的协同作用可以显著增加量子相干性的最大值，并明显减缓其衰减速率。在铁磁情形与反铁磁情形中都发现当外磁场B <0时，量子相干性存在的温度范围更大，更有利于保存量子相干性。     

带有Dzyaloshinski-Mariya相互作用的两比特XXZ模型的纠缠量子热机

以带有Dzyaloshinski-Mariya 相互作用的两比特XXZ模型为工作物质构建纠缠量子热机. 在量子热力学平衡态下, 采用Kieu的形式描述了做功与热传递.对于不同的各向异性参数, 分析了热机循环中量子纠缠与热传递、做功以及机械效率等热力学量之间的关系. 结果表明: 在这个纠缠体系中, 热力学第二定律依然成立; 机械效率的等值线图是环状曲线; 当各向异性参数Δ较小时, 热机在C₁ > C₂ 和C₁ < C₂ 两区域运行, 当增大Δ值时, 热机只在C₁ > C₂ 区域运行. 关键词： 量子热机 并发度 机械效率     

不同磁场环境下Heisenberg XXZ自旋链中的热量子失协

本文研究了不同磁场环境下一维Heisenberg XXZ自旋链中两量子比特的热量子失协特性. 在四种不同的磁场环境下: 1) B₁=B₂=0 (无磁场); 2) B₁≠0, B₂=0 (磁场只作用于其中一个量子比特); 3) B₁=B₂ (均匀磁场); 4) B₁=-B₂ (非均匀磁场), 对分别作用在每个量子比特上的磁场B₁和B₂对其量子关联的影响作了详细的讨论, 且数值计算和比较了其量子失协和量子纠缠的异同. 结果显示: 在有限温度下, 量子失协相比于量子纠缠更普遍, 且非均匀磁场相比于均匀磁场对量子失协和量子纠缠更有用, 更有利于量子通讯和量子信息处理过程. 关键词： 量子关联 纠缠 量子失协     

On quantum solitons and their classical relatives: Bethe Ansatz states in soliton sectors of the sine-Gordon system

Previously we have found that the semiclassical sine-Gordon/Thirring spectrum can be received in the absence of quantum solitons via the spin $\text{1}\text{2}$ approximation of the quantized sine-Gordon system on a lattice. Later on, we have recovered the Hilbert space of quantum soliton states for the sine-Gordon system. In the present paper we present a derivation of the Bethe Ansatz eigenstates for the generalized ice model in this soliton Hilbert space. We demonstrate that via “Wick rotation” of a fundamental parameter of the ice model one arrives at the Bethe Ansatz eigenstates of the quantum sine-Gordon system. The latter is a “local transition matrix” ancestor of the conventional sine-Gordon /Thirring model, as derived by Faddeev et al. within the quantum inverse-scattering method. Our result is essentially based on the N < ∞, Δ = 1, m ? 1 regime. Consequently, the spectrum received, though resembling the semiclassical one, does not coincide with it at all.     

Sine-Gordon Model: Renormalization Group Solution and Applications

The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is obtained and discussed in detail. The gap in this theory is estimated in terms of the sine-Gordon model parameters. The mapping between the sine-Gordon model and one-dimensional interacting-electron models, such as the g-ology and Hubbard models, is discussed. On the basis of the results borrowed from previous renormalization-group results for the sine-Gordon model, different aspects of Luttinger liquid systems are described, such as the nature of the excitations and phase transitions. The calculations are thoroughly and pedagogically described, to even reach the reader with no previous experience with the sine-Gordon model or the renormalization group approach.     

A nonlocal Poisson bracket of the sine-Gordon model

It is well known that the classical string on a two-sphere is more or less equivalent to the sine-Gordon model. We consider the non-abelian dual of the classical string on a two-sphere. We show that there is a projection map from the phase space of this model to the phase space of the sine-Gordon model. The corresponding Poisson structure of the sine-Gordon model is nonlocal with one integration.     

On non-equilibrium states in QFT model with boundary interaction

We prove that certain non-equilibrium expectation values in the boundary sine-Gordon model coincide with associated equilibrium-state expectation values in the systems which differ from the boundary sine-Gordon in that certain extra boundary degrees of freedom (q-oscillators) are added. Applications of this result to actual calculation of non-equilibrium characteristics of the boundary sine-Gordon model are also discussed.     

Macroscopic Quantum Coherence of an Antiferromagnetic Spin Chain with Biaxial Anisotropy in an External Magnetic Field

We in this paper provide a sine-Gordon model of (1+1)-dimensions in which macroscopic quantum coherence of domain walls may be observed. The tunneling amplitude in field models of (1+1)-dimensions, such as sine-Gordon, is negligible small at zero temperature. In the long, but finite-length chain at finite temperature it is possible to have a finite, but still very small one. In the present model of the antiferromagnetic spin chain with biaxial anisotropy in an external magnetic field, in which the height of the sine-Gordon barrier can be tuned, the tunneling amplitude is shown to be enhanced by adjusting the external parameter.     

Quantization of solitons and the restricted sine-Gordon model

We show how to compute form factors, matrix elements of local fields, in the restricted sine-Gordon model, at the reflectionless points, by quantizing solitons. We introduce (quantum) separated variables in which the Hamiltonians are expressed in terms of (quantum) τ-functions. We explicitly describe the soliton wave functions, and we explain how the restriction is related to an unusual hermitian structure. We also present a semi-classical analysis which enlightens the fact that the restricted sine-Gordon model corresponds to an analytical continuation of the sine-Gordon model, intermediate between sine-Gordon and KdV. Laboratoire associé au CNRS. Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique.     

LargeThe Coleman Phage Transition in Double Sine-Gordon Model

The Gaussian effective potential of the double sine-Gordon mode in 1+1 dimensions is calculated within this approximation, a Coleman phase transition condition is obtained which reduces to the well-known result in sine-Gordon model.     

The Kondo Problem as the Quantum Sine-Gordon Model

The ground-state properties of the Kondo Hamiltonian is analyzed in detail and we find the problem to be exactly equivalent to a modified quantum sine-Gordon model. Paralleling to the renormalization-group theory of the sine-Gordon model, we easily derive the correct next-to-leading order flow equations and obtain a universal quantity in a linear combination of the coefficients of the higher-order terms.     

On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between the coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin–Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model with the fermion number. Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001