一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

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.     

Fidelity in topological superconductors with end Majorana fermions

Fidelity and fidelity susceptibility are introduced to investigate the topological superconductors with end Majorana fermions. A general formalism is established to calculate the fidelity and fidelity susceptibility by solving Bogoliubov–de Gennes equations. Both clean and disordered systems are studied within this formalism, and the results show that the fidelity susceptibility serves as a valid indicator for the topological quantum phase transition which signals the appearance of Majorana fermions. Our study provides a useful tool to investigate the topological quantum phase transition in superconductors, which is helpful to find topological phases in various systems.     

Critical Dynamics of Transverse-field Quantum Ising Model using Finite-Size Scaling and Matrix Product States

The study of phase transition is usually done by numerical simulation of finite system. Conventional methods such as Monte Carlo simulations and phenomenological renormalization group methods obtain the critical exponents without obtaining the quantum wavefunction of the system. The Matrix Product States formalism allows one to obtain accurate numerical wavefunctions of short ranged interacting quantum many-body systems. In this study we combine the Finite Size Scaling theory and Matrix Product States formalism to study the critical dynamics of one-dimensional quantum Ising model. Finite size simulations of 20, 40, 60, 80, 100 and 120 spins are done using the Density Matrix Renormalization Group to obtain the ground state wavefunction of the system. The thermodynamic quantities such as the magnetization, susceptibility and correlation function are calculated. The critical exponents independently calculated are respectively β/ν = 0.1235(1), γ/ν = 1.7351(2), and η = 0.249(1). They conform with the theoretical values from analytical solution and fulfil the hyperscaling relation. We showed that both methods combined can reliably study the critical dynamics of one-dimensional Ising-like quantum lattice systems. Application of the study on water-ice phase transition of single-file water in nanopores is proposed.

     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Contracted Hamiltonian on Symmetric Space <Emphasis Type="Italic">SU</Emphasis>(3)/<Emphasis Type="Italic">SU</Emphasis>(2) and Conserved Quantities

We study the quantum model on symmetric space SU(3)/SU(2). By using the Inonu-Wigner contraction to Lie algebra su(3), we arrive at a special case of three-body Sutherland model. It has shown that by calculating conservative quantities of this model, it has Poincare Lie algebra, too.     

Fidelity spectrum: A tool to probe the property of a quantum phase

Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points,information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum. By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the twodimensional Kitaev model on a honeycomb lattice. It was found that the spectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.     

An algebraic description of anharmonic diatom–diatom inelastic collisions in the semiclassical approximation

An algebraic model to describe inelastic collisions between two anharmonic diatomic molecules in the semiclassical approximation is presented. The interactions for the diatomic systems are modelled in terms of Morse potentials, while an exponential repulsive potential is taken for the interactions between the nearest atoms of the diatomic systems. This problem is treated in the interaction potential framework, where an approximation in terms of the generators of three SU(2) groups is proposed, two corresponding to the Morse oscillators and the other to the interaction. The transition probabilities are given in terms of a sum of the products of three Wigner's d(β) functions corresponding to the three SU(2) groups. As an example the systems N₂?+?N₂ and H₂?+?H₂ are described and compared with exact quantum mechanical calculations.     

多粒子GHZ纠缠实验中Fisher信息的保真度方法获取

保真度与Fisher信息在量子精密测量和量子纠缠判定中充当着非常重要的角色。本文从概率统计和量子力学的角度出发,阐明了两者之间的区别与联系,给出了保真度方法获取Fisher信息的数学表达式;基于量子测量中常见的宇称测量模型,我们对多粒子Greenberger-Horne-Zeilinger (GHZ)纠缠产生实验中Fisher信息的获取开展了保真度方法研究,通过对实验数据的蒙特卡洛模拟,二阶或高阶曲线拟合获取了系统的Fisher信息,并将其与理论计算结果进行对比,结果表明保真度方法可以有效地获取量子系统的Fisher信息,当体系粒子数目较少时,宜采用二阶拟合方法获取系统的Fisher信息,而当粒子数目较多时,需考虑高阶拟合项的影响。此外,我们还将多光子GHZ纠缠实验中Fisher信息的保真度获取结果与海林格距离方法的获取结果进行对比,发现二者是一致的,这也进一步验证了保真度方法获取Fisher信息的有效性。本文的研究也为开展与Fisher信息相关的量子拓扑学和量子相变的研究提供了新的途径。     

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.     

Wave functions and spectrum in hot electroweak matter for large Higgs masses

We present results for the wave functions and the screening mass spectrum for quantum numbers , and in the three-dimensional SU(2)–Higgs model near to the phase transition line below the endpoint and in the crossover region. Varying the 3D gauge couplings we study the behaviour along a line of constant physics towards the continuum limit in both phases. In the crossover region the changing spectrum of screening states versus temperature is examined showing the aftermath of the phase transition at lower Higgs mass. Different to smearing concepts we used large sets of operators with various extensions allowing to identify wave functions in position space. Received: 4 August 1998 / Published online: 2 November 1998     

Phase transitions in quark matter and behaviour of physical observables in the vicinity of the critical end point

We study the chiral phase transition at finite T and μ _B within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite temperature and baryonic chemical potential are investigated: the study of physical quantities, such as the baryon number susceptibility near the CEP, will provide complementary information concerning the order of the phase transition. We also analyze the information provided by the study of the critical exponents around the CEP.     

Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.     

Diagonal entropy in many-body systems: Volume effect and quantum phase transitions

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbor interactions. We focus on the DE of a subsystem of L continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.     

二维３态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态 (iPEPS) 算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维３态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态算法(iPEPS),在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还开创性提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维3态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态(i PEPS)算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于i PEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

Λ型三能级原子与两个谐振器的量子相位门

量子纠缠的生成和操控在量子通信和量子信息处理中具有广泛的应用价值.通过构建单个Λ型三能级原子和两个超导谐振器之间相互耦合的模型,给出了实现控制Z门(Controlled-Z)的四种操作方案和实现交换门(Swap)的两种操作方案;同时对实现控制Z门的第一种操作方案进行了保真度的数值模拟仿真.结果表明:通过20.83 ns的运行时间,其保真度为96.67%,而衰减率、弛豫速率和移相比率的增加会降低系统的保真度,而耦合强度的增加会减少系统的运行时间,从而减小衰减参数的影响,提高系统的保真度.     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.