量子相变与量子纠缠

作为量子体系一种内在的非局域性关联,量子纠缠已经成为一个可利用的重要资源并广泛应用于许多领域.强关联体系中的量子相变,作为凝聚态理论中的一个重要现象,也一直是人们研究的热点.本文介绍了量子纠缠的定义,纠缠的判据,以及纠缠的度量.接着,通过一个具体模型对如何利用量子纠缠描述量子相变进行讨论和分析.研究发现,在强关联体系量子相变中量子纠缠扮演着非常重要的角色.     

量子相变和量子临界现象

本文综述凝聚态物理学中的量子相变和量子临界现象,首先考察了相变中存在量子效应的可能性,通过横磁场Ising模型介绍了量子相变的基本特征;接下来对照热临界现象,引入了量子标度和量子重正化的基本概念和操作方式;然后利用量子临界现象的方案,分析了密度驱动、无序驱动和关联驱动的金属-绝缘体相变;继续利用量子临界性的概念探讨如重电子化合物、铜氧化物和巡游铁磁体这类复杂的相互作用多粒子系统;最后选择量子点、碳纳米管和单层石墨为例,介绍了量子临界性在低维和纳米系统研究中的作用.     

保真率与量子相变

量子相变是量子多体理论中的一个重要概念,保真度则是量子信息学的重要概念.文章简单介绍了一个量子系统的基态对系统参量的响应,即保真率,在量子相变中的行为.作为理解量子相变的一个新的视角,保真度方法的优势在于它是一个纯粹的几何学量,所以在研究相变过程中不需要考虑任何预设的序参量.文章用通俗的语言介绍了基态保真度、保真率、量子绝热维度以及它们的物理意义.为便于理解,文章以Lipkin-Meshkov-Glick模型与Kitaev蜂巢模型为例,对保真率在这两个模型中的性质做了简单介绍.     

双模Dicke模型的一级量子相变

多光场与多粒子相互作用的多模Dicke模型不但存在着更为丰富的量子相,而且在量子信息中有着重要的应用.本文运用Holstein-Primakoff变换和玻色扩展法研究双模Dicke模型的基态特性并从理论上发现了一个新的一级量子相变.该相变在实验上可以通过测量平均光子数或原子布居数进行观察.     

二维伊辛模型相变临界点温度的模拟计算

用计算模拟方法计算了二维伊辛模型的相变临界点温度,其结果接近严格解,明显布喇格－威廉斯近似和贝特近似的结果。     

原子核过渡区的量子相变

在相互作用玻色子模型(IBM) 基础上用O(6) 高阶项代替传统的SU(3) 四极-四极相互作用来研究原子核从振动到转动过渡区的量子相变行为。利用U(5)-SU(3) 和UQ 两种方案,在玻色子数分别为N = 8 和N = 20 不同情况下,研究了原子核的一些低激发态的能级比和电四极跃迁比。结果表明:随着玻色子数N 的增大,系统的量子相变行为得到加强;两种方案都可以用来描述从振动到转动过渡区的原子核的量子相变特征且O(6) 高阶项方案下量子相变行为更为明显。在此基础上,进一步应用这两种方案具体讨论了152Sm 核的低激发态能级和电四极跃迁性质并与实验数据进行对比分析。结果表明,用O(6) 高阶项可以更为合理地描述带内跃迁及不同带之间的带间跃迁性质。With the framework of Interacting Boson Model(IBM), transitional patterns from the spherical to the axially deformed limit of the IBM with a schematic Hamiltonian are studied by replacing the SU(3) quadrupole-quadrupole term with O(6) cubic interaction. But, we use the two schemes to investigate some energy ratios and B(E2) ratios for different bosons N = 8 and N = 20. The results show that with the increasing of the numbers of bosons, the transitional behaviors can be enhanced; the transitional behaviors are very similar in the two schemes. However, there are some distinctive differences for some quantities across the entire transitional region, such as energy levels and ratios, B(E2) values and ratios, and expectation values of the shape variables. Generally speaking, the transition is smoother and the nuclear shape is less well defined in the new scheme. Then we apply the two schemes to the critical point symmetry candidate, such as 152Sm, and find the overall fitting quality of the UQ scheme is better than that of the U(5)-SU(3) scheme, especially for the inter-band E2 transitions in 152Sm.     

磁性量子相变

量子相变广泛存在于关联电子材料体系中,与非常规超导和奇异金属行为有着紧密的联系。近年来,人们对量子相变的认识正在不断深入,不同类型的量子相变相继被发现。揭示量子相变的普适分类,发展和完善量子相变理论,探索量子临界点附近的呈展量子态及其产生机理是当前量子相变研究的热点。文章简要介绍磁性量子相变的一些最新研究进展以及面临的挑战。     

量子相变与几何相位

量子相变是凝聚态物理中的重要研究课题,而几何相位的发现是近几十年来量子力学中的重要进展,它们毫无关联地各自发展.但最近的研究表明,它们之间有密切联系：多体体系基态的几何相位在量子相变点附近具有标度性;不可收缩的几何相位可用来作为量子相变的标志等.文章将介绍最近在量子相变和几何相位的关系方面的研究进展,并用XY自旋链模型来详细说明.这些结果应会吸引凝聚态和几何相位领域工作的研究人员的关注和兴趣.     

Kitaev模型与拓扑量子相变

文章通过在一种准一维路径上引入自旋算符的约当-维格纳（Jordan—Wigner）变换，证明了Kitaev自旋模型完全等价于一个不含任何非物理自由度的自由Majorana费米子模型。通过对偶变换，进一步证明了这个系统中存在的量子相变可用非定域的拓扑序参量来描述；并且，这些非定域的拓扑序参量在对偶空间变成为定域的朗道类型的序参量。文章作者的工作揭示了传统的量子相变和拓扑量子相变的内在关系，扩展了朗道二级相变理论的适用范围。     

Phase transitions and relaxation characteristics of Quantum Magnets and Quantum Glasses

An overview is presented of the phase changes as well as certain relaxation characteristics of model quantum magnets, magnetic glasses and proton glasses. Although the systems considered are quite varied, they are connected by the common themes of tunneling, transverse Ising model, long-ranged interactions and above all, the occurrence of quantum phase transitions. Because the interactions are long-ranged, mean-field theory is eminently suitable for analyzing both the equilibrium and nonequilibrium properties. Wherever pertinent, detailed comparisons with experimental data have been presented.     

Quantum phase transitions in antiferromagnets and superfluids

We present a general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition. Basic results are reviewed in the context of experiments on the spin-ladder compounds, insulating two-dimensional antiferromagnets, and double-layer quantum Hall systems. Recent large N computations on an extended t–J model (Phys. Rev. Lett. 83 (1999) 3916) motivate a global scenario of the quantum phases and transitions in the high-temperature superconductors, and connections are made to numerous experiments.     

Quantum phase transitions in mesoscopic Rashba rings

Novel quantum phases are found in the ground state of Rashba ring: the orbital magnetic phase (OMP), non-OMP, pseudo-OMP and quasi-OMP, which depend on the spin-orbit interaction (SOI) strength, electron number and ring size. We give the phase diagram and their quantum-phase-transition conditions.     

Overview of phases and phase transitions

We provide an overview of some modern developments in the theory of phases and phase transitions in classical and quantum systems. We show the link between non-ergodicity and fidelity in quantum systems and discuss topological phase transitions. We show that the quantum phase transitions are associated with qualitative changes in some properties of the quantum wavefunctions across the phase transition. We discuss the topological phase transition associated with p-wave superconductor since it is a topic of wide interest because of the possible observation of Majorana fermions.     

Quantum phase transitions in Bose-Einstein condensates from a Bethe ansatz perspective

We investigate two solvable models for Bose-Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of both models, as we vary some parameters of the Hamiltonian, suggests a connection between the behavior of the roots of the Bethe ansatz equations and the physical behavior of the models. Then, by the use of standard techniques for approaching quantum phase transition - gap, entanglement and fidelity - we find that the change in the scenery in the roots of the Bethe ansatz equations is directly related to a quantum phase transition, thus providing an alternative method for its detection.     

Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H ₀ )ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.     

Frustration and quantum phase transitions in an anisotropic antiferromagnet on a square lattice

We study the effect of frustration between nearest and next-nearest neighbors of the quantum S=1 anisotropic Heisenberg model on a square lattice using the bond operator technique. A single-site anisotropy term induces a quantum phase transition in the system. We calculate the effect of zero-temperature quantum fluctuations on the magnetization for the Néel and collinear antiferromagnetic phases.