Long-range quantum discord in critical spin systems

We show that quantum correlations as quantified by quantum discord can characterize quantum phase transitions by exhibiting nontrivial long-range decay as a function of distance in spin systems. This is rather different from the behavior of pairwise entanglement, which is typically short-ranged even in critical systems. In particular, we find a clear change in the decay rate of quantum discord as the system crosses a quantum critical point. We illustrate this phenomenon for first-order, second-order, and infinite-order quantum phase transitions, indicating that pairwise quantum discord is an appealing quantum correlation function for condensed matter systems.     

Quantum phase transitions in electronic systems

Quantum phase transitions occur at zero temperature when some non‐thermal control‐parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a pedagogical introduction to quantum phase transitions and quantum critical behavior emphasizing similarities with and differences to classical thermal phase transitions. We then illustrate the general concepts by discussing a few examples of quantum phase transitions occurring in electronic systems. The ferromagnetic transition of itinerant electrons shows a very rich behavior since the magnetization couples to additional electronic soft modes which generates an effective long‐range interaction between the spin fluctuations. We then consider the influence of rare regions on quantum phase transitions in systems with quenched disorder, taking the antiferromagnetic transitions of itinerant electrons as a primary example. Finally we discuss some aspects of the metal‐insulator transition in the presence of quenched disorder and interactions.     

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

We investigate quantum phase transitions for q-state quantum Potts models (q=2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen-Shannon divergence, the relative entropy of coherence, and the l₁ norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.     

Effect of intersite repulsion on the correlation functions and thermodynamics of an Ising chain with annealed magnetic disorder

An exact solution for a model describing the equilibrium behavior of an ensemble of Ising chains with nonmagnetic intersite repulsion of nearest neighbors and an equilibrium distribution of nonmagnetic impurities is obtained using the transfer matrix technique. The possibility of exciting quantum phase transitions using the intersite repulsion parameter in a system is demonstrated. Proximity to the critical points of these transitions has a substantial effect on the temperature dependence of a system’s magnetic susceptibility.     

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.     

Quantum critical end point for the Kondo volume collapse model

The Kondo volume collapse describes valence transitions in f-electron metals and is characterized by a line of first order transitions in the pressure-temperature phase plane terminated at critical end points. We analyze the quantum critical end point, when the lower end point is tuned to T=0, and determine the specific heat, thermal expansion, and compressibility. We find that the inclusion of quantum critical fluctuations leads to a novel bifurcation of the first order phase line. Finally, we show that critical strain fluctuations can cause both, superconductivity and non-Fermi liquid behavior near the critical point.     

一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.     

Alternative approach to thermodynamic phase transitions

One of the major open problems in theoretical physics is the lack of a consistent quantum gravity theory.Recent developments in our knowledge on thermodynamic phase transitions of black holes and their van der Waalslike behavior may provide an interesting quantum interpretation of classical gravity.Studying different methods of investigating phase transitions can extend our understanding of the nature of quantum gravity.In this paper,we present an alternative theoretical approach for finding thermodynamic phase transitions in the extended phase space.Unlike the standard methods based on the usual equation of state involving temperature,our approach uses a new quasiequation constructed from the slope of temperature versus entropy.This approach addresses some of the shortcomings of the other methods and provides a simple and powerful way of studying the critical behavior of a thermodynamical system.Among the applications of this approach,we emphasize the analytical demonstration of possible phase transition points and the identification of the non-physical range of horizon radii for black holes.     

Ordered State and Superfluidity of Quasi-Two-Dimensional Excitons in Type-II Quantum Wells

One of the best ways to obtain unambiguous experimental evidence for the superfluidity of excitons is to observe phenomena that are directly related to the phase of the condensed excitons. As an advantageous candidate for this purpose, we propose a quasi-two-dimensional exciton system in type-II quantum wells (QWs). We consider the condensed excitons in the type-II QW irradiated by a weak laser light and show that under the control of an external current J ex , the system takes the ordered state with (without) net superflow of excitons at T = 0 K when J ex is larger (smaller) than a certain critical value. Introducing probable mechanisms of phase transitions, we calculate the transition temperatures and construct the phase diagram.     

含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度

利用张量网络表示的无限矩阵乘积态算法研究了含有Dzyaloshinskii-Moriya (DM)相互作用的键交替海森伯模型的量子相变和临界标度行为.基于矩阵乘积态的基态波函数计算了系统的量子纠缠熵及非局域拓扑序.数据表明,随着键交替强度变化,系统从拓扑有序的Haldane相转变为局域有序的二聚化相.同时DM相互作用抑制了系统的二聚化,并最终打破系统的完全二聚化.另外,通过对相变点附近二聚化序的一阶导数和长程弦序的数值拟合,分别得到了此模型相变的特征临界指数a和b的值.结果表明,随着DM相互作用强度的增强, a逐渐减小,同时b逐渐增大. DM相互作用强度影响着此模型的临界行为.针对此模型的临界性质的研究,揭示了量子自旋相互作用的彼此竞争机制,对今后研究含有DM相互作用的自旋多体系统中拓扑量子相变临界行为提供一定的借鉴与参考.     

Thermal expansion and Grüneisen parameters of Ba(Fe(1-x)Co(x))2As2: a thermodynamic quest for quantum criticality

Thermal expansion data are used to study the uniaxial pressure dependence of the electronic-magnetic entropy of Ba(Fe(1-x)Co(x))2As2. Uniaxial pressure is found to be proportional to doping and, thus, also an appropriate tuning parameter in this system. Many of the features predicted to occur for a pressure-tuned quantum critical system, in which superconductivity is an emergent phase hiding the critical point, are observed. The electronic-magnetic Grüneisen parameters associated with the spin-density wave and superconducting transitions further demonstrate an intimate connection between both ordering phenomena.     

On the equivalence between magnetic-field-induced phase transitions in the integer quantum Hall effect

Magnetic-field-induced phase transitions in the two-dimensional electron system in a AlGaAs/InGaAs/GaAs heterostructure are studied. Two kinds of magnetic-field-induced phase transitions, plateau-plateau (P-P) and insulator-quantum Hall conductor (I-QH) transitions, are observed in the integer quantum Hall effect regime at high magnetic fields. In the P-P transition, both the semicircle law and the universality of critical conductivities are broken and we do not observe the universal scaling. However, the P-P transition can still be mapped to the I-QH transition by the Landau-level addition transformation, and as the temperature decreases the critical points of these two transitions appear at the same temperature. Our observations indicate that the equivalence between P-P and I-QH transitions can be found by the suitable analysis even when some expected universal properties are invalid.     

Disorder promotes ferromagnetism: rounding of the quantum phase transition in Sr(1-x)Ca(x)RuO3

The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases. Particularly strong disorder effects have been predicted to occur at zero-temperature quantum phase transitions. Here, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in Sr(1-x)Ca(x)RuO3 is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. Using a magneto-optical technique, we map the magnetic phase diagram in the composition-temperature space. We find that the ferromagnetic phase is significantly extended by the disorder and develops a pronounced tail over a broad range of the composition x. These findings are explained by a microscopic model of smeared quantum phase transitions in itinerant magnets. Moreover, our theoretical study implies that correlated disorder is even more powerful in promoting ferromagnetism than random disorder.     

Dynamics of a quantum phase transition: exact solution of the quantum Ising model

The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.     

Nonequilibrium quantum criticality in open electronic systems

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant-electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions.     

Detecting quantum critical points using bipartite fluctuations

We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state-of-the-art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows us to find quantum critical points with much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.     

Quantum phase transition by employing trace distance along with the density matrix renormalization group

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs.     

MaxEnt and dynamical information

The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect.     

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.