Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains:Effect of the Dzyaloshinski-Moriya interaction

We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya (DM) interaction, and investigate the effect of the DM interaction on the quantum phase transition (QPT) of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.     

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence(SC) and square of quantum discord(SQD). The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.     

横场中具有周期性各向异性的一维XY模型的量子相变

通过解析和数值计算的方法研究了横场中具有周期性各向异性的一维XY自旋模型的量子相变和量子纠缠.主要讨论了周期为二的情况,即各向异性参数交替地取比值为α的两个值.结果表明,与横场中均匀XY模型相比,α=-1所对应的模型在参数空间的相图存在着明显的不同.原来的Ising相变仍然存在,没有了沿x和y方向的各向异性铁磁(FM_x,FM_y)相,即各向异性相变消失,出现了一个新的相,并且该相内沿x和y方向的长程关联函数相等且大于零,我们称新相为各向同性铁磁(FM_(xx))相.这是由于系统新的对称性所导致的.解析结果还说明系统在FM_(xx)相中的单粒子能谱有两个零点,是一个无能隙的相.最后,利用冯·诺依曼熵数值地研究了系统在新相内各点的量子纠缠,发现该相内每一点的冯·诺依曼熵的标度行为与均匀XY模型在各向异性相变处的相似,即S_L～1/3㏒_2L+Const.     

一维化学势调制的p波超导体中的拓扑量子相变

本文研究了一维公度势和非公度势调制下的p波超导量子线系统的拓扑相变.在公度势调制下,通过计算Z2拓扑不变量确定系统的相图,指出系统的拓扑相变强烈地依赖于调制参数α和相移δ.在非公度势调制下,以α=(√5-1)/2,δ=0为例,计算系统的低能激发谱、Z2拓扑不变量以及逆参与率等,发现p波配对强度△∈(0,0.33)时,系统存在拓扑非平庸超导相,拓扑平庸超导相和拓扑平庸局域相的转变.而当p波配对强度△>0.33时,系统存在拓扑非平庸超导相和拓扑平庸局域相的转变.     

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。     

Picturing quantum phase transitions

We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlations in the vicinity of the critical points are analyzed both in the ground states and low temperature thermal states.     

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.     

Superconducting phase transitions in quantum dots

In NdN and SdS nanostructures, anomalous ground states with a non-integer average number of electrons in the quantum dots d occur. These states correspond to pair or single-electron superconductivity and are separated from states with a definite (integer) number of electrons by, as a rule, second-order phase transitions. The characteristic features of the pair and single-electron superconducting Josephson current in SdS are discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 618–623 (10 November 1996)     

Self-duality in superconductor-insulator quantum phase transitions

It is argued that close to a Coulomb interacting quantum critical point the interaction between two vortices in a disordered superconducting thin film separated by a distance r changes from logarithmic in the mean-field region to 1/r in the region dominated by quantum critical fluctuations. This gives support to the charge-vortex duality picture of the observed reflection symmetry in the current-voltage characteristics on both sides of the transition.     

Ground-state phases and quantum phase transitions in a two-dimensional spin-1/2 XY model with four-spin interactions

We discuss the ground state phase transition between an antiferromagnet and a valence-bond solid in a two-dimensional spin-1/2 XY model with a four-spin interaction. This transition has been proposed as a candidate for a deconfined quantum-critical point. We analyze quantum Monte Carlo data in order to accurately characterize the transition. The central question that remains to be answered is whether the transition really is continuous, or whether it is actually weakly first-order. We present the current status of both ground state and finite-temperature calculations. Based on the results, we discuss possible scenarios for the transition, none of which is consistent with deconfined quantum-criticality. However, we argue that a deconfined quantum-critical point may be located nearby in an extended parameter space.We also discuss the staggered Ising phase obtaining in the limit of strong four-spin coupling.     

Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.     

Effects of quantum entanglement in phase transitions

Starting with the canonical ensemble over the space of pure quantum states, we obtain an integral representation for the associated partition function. This is used to calculate the magnetisation of a system of N spin- particles. The results suggest the existence of a first order phase transition that occurs at zero temperature in the absence of spin-spin interactions.     

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.     

Theory of smeared quantum phase transitions

We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.     

Weak first-order superfluid-solid quantum phase transitions

We study superfluid-solid zero-temperature transitions in two-dimensional lattice boson-spin models using worm-algorithm Monte Carlo simulations. We observe that such transitions are typically first order with the exception of special high-symmetry points which require fine-tuning in the Hamiltonian parameter space. We present evidence that the superfluid-checkerboard solid and superfluid-valence-bond solid transitions at half-integer filling factor are extremely weak first-order transitions and in small systems can be confused with continuous or high-symmetry points.     

Striped phase in a quantum XY model with ring exchange

We present quantum Monte Carlo results for a square-lattice S=1/2 XY model with a standard nearest-neighbor coupling J and a four-spin ring exchange term K. Increasing K/J, we find that the ground state spin stiffness vanishes at a critical point at which a spin gap opens and a striped bond-plaquette order emerges. At still higher K/J, this phase becomes unstable and the system develops a staggered magnetization. We discuss the quantum phase transitions between these phases.