Global quantum discord and quantum phase transition in XY model

We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global quantum discord (GQD) and the corresponding quantum correlations. We demonstrate that the maximum of the sum of all the nearest neighbor bipartite GQDs is effective and accurate for signaling the Ising quantum phase transition, in contrast, the sudden change of GQD is very suitable for characterizing another phase transition in the XY model. This may shed lights on the study of properties of quantum correlations in different quantum phases.     

LMG model: Markovian evolution of classical and quantum correlations under decoherence

We have investigated the quantum phase transition in the ground state of collective Lipkin-Meshkov-Glick model (LMG model) subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. We discuss the behavior of quantum and classical pair wise correlations in the system, with the quantumness of correlations measured by quantum discord (QD), entanglement of formation (EOF), measurement-induced disturbance (MID) and the Clauser-Horne-Shimony-Holt-Bell function (CHSH-Bell function). The time evolution established by system-environment interactions is assumed to be Markovian in nature and the quantum channels studied include the amplitude damping (AD), phase damping (PD), bit-flip (BF), phase-flip (PF), and bit-phase-flip (BPF) channels. One can identify appropriate quantities associated with the dynamics of quantum correlations signifying quantum phase transition in the model. Surprisingly, the CHSH-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.     

Geometric phase and quantum phase transition in the Lipkin–Meshkov–Glick model

The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin–Meshkov–Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this model. The possibility of the geometric phase or its derivatives as the universal order parameter of characterizing quantum phase transitions has been also discussed.     

Dynamical Suppression of Decoherence in Two-Qubit Quantum Memory

In this paper, we have detailedly studied the dynamical suppression of the phase damping for the two-qubit quantum memory of Ising model by the quantum “bang-bang” technique. We find the sequence of periodic radio-frequency pulses repetitively to flip the state of the two-qubit system and quantitatively find that these pulses can be used to effectively suppress the phase damping decoherence of the quantum memory and freeze the system state into its initial state. The general sequence of periodic radio-frequency pulses to suppress the phase damping of multi-qubit of Ising model is also given.     

Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.     

光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.     

Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic field is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti-Jaynes-Cummings (AJC) or Jaynes-Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic field) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit.     

Path Integral Approach of Quantum Heisenberg Planar Spin Glass Model in the Presencesof Random Field

A quantum version of the site-random Heisenberg planar XY model in a random field is presented in the boson representation. Like classical spherical model in the spin space, the model can be solved exactly within the coherent state path integral-representation. The phase diagram is obtained, and the effects of the randomness and quantum fluctuations on the onset of a spin glass phase are discussed.     

Ground-state entanglement in a three-spin transverse Ising model with energy current

The ground-state entanglement associated with a three-spin transverse Ising model is studied. By introducing an energy current into the system, a quantum phase transition to energy-current phase may be presented with the variation of external magnetic field; and the ground-state entanglement varies suddenly at the critical point of quantum phase transition. In our model, the introduction of energy current makes the entanglement between any two qubits become maximally robust.     

Mott insulator-superfluid phase transition in a detuned multi-connected Jaynes-Cummings lattice

The connectivity and tunability of superconducting quantum devices provide a rich platform to build quantum simulators and study novel many-body physics. Here we study quantum phase transition in a detuned multi-connected Jaynes-Cummings lattice, which can be constructed with superconducting circuits. This model is composed of alternatively connected qubits and cavity modes.Using a numerical method, we show that by varying the detuning between the qubits and the cavities, a phase transition from the superfluid phase to the Mott insulator phase occurs at commensurate fillings in a one-dimensional array. We study the phase transition in lattices with symmetric and asymmetric couplings, respectively.     

Geometric phase for adiabatic evolutions of general quantum states

The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.     

Amplitude phase-space model for quantum mechanics

We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.     

Scaling of geometric phases close to the quantum phase transition in the XY spin chain

We show that the geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.     

Dicke模型的量子经典对应关系

非旋波近似条件下Dicke模型表现为量子混沌动力学特征.在详细考察Dicke模型经典相空间结构特点的基础上,采用经典-量子"一对多"的思想,即经典相空间中的一点对应于量子体系两个初始相干态的演化,利用对两个初态量子纠缠动力学演化取统计平均的方法,得到了与经典相空间对应非常好的量子相空间结构.数值计算结果表明:经典混沌有利地促进系统两体纠缠的产生,平均纠缠可以作为量子混沌的标识,利用平均纠缠可以得到一种较好的量子动力学与经典相空间的对应关系. 关键词： Dicke模型 非旋波近似 量子混沌 经典量子对应     

Resonating plaquette phase of a quantum six-vertex model

The simplest quantum generalization of the six-vertex model describes fluctuations of the order parameter of the d-density wave (DDW), believed to compete with superconductivity in the high-T(c) superconductors. The ground state of this model undergoes a first order transition from the DDW phase to a resonating plaquette phase as the quantum fluctuations are increased, which is explored with the help of quantum Monte Carlo simulations and analytic considerations involving the n-vector (n = 2) model with cubic anisotropy. In addition to finding a new quantum state, we show that the DDW is robust against a class of quantum fluctuations of its order parameter. The inferred finite temperature phase diagram contains unsuspected multicritical points.     

Effective Interactions Due to Quantum Fluctuations

A class of quantum lattice models is considered, with Hamiltonians consisting of a classical (diagonal) part and a small off-diagonal part (e.g. hopping terms). In some cases when the classical part has an infinite degeneracy of ground states, the quantum perturbation may stabilize some of them. The mechanism of this stabilization stems from effective potential created by the quantum perturbation. Conditions are found when this strategy can be rigorously controlled and the low temperature phase diagram of the full quantum model can be proven to be a small deformation of the zero temperature phase diagram of the classical part with the effective potential added. As illustrations we discuss the asymmetric Hubbard model and the Bose–Hubbard model. Received: 28 April 1998 / Accepted: 19 March 1999     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

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。     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method. The bond-alternative effects on its ground-state phase diagram are discussed in detail. Once the bond alternation is taken into account, the antiferromagnetic phase (Δ > 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order. The QPT is shown to be second-order, and the whole phase diagram is provided. For the ferromagnetic phase region (Δ < -1), the critical point r^c always equals 1 (independent of Δ), and the QPT for this case is shown to be first-order. The dimerized Heisenberg model is also discussed, and two disordered phases can be distinguished by with or without nonlocal string orders. Both the bipartite entanglement and the fidelity per site, as two kinds of model-independent measures, are capable of describing all the QPTs in such a quantum model.