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.     

Interplay of Quantum and Classical Fluctuations Near Quantum Critical Points

For a system near a quantum critical point (QCP), above its lower critical dimension d _L , there is in general a critical line of second-order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, d _eff?=?d?+?z (d is the Euclidean dimension of the system and z the dynamic quantum critical exponent) is above its upper critical dimension $d_{_{C}}$ there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation ψ?=?νz between the shift exponent ψ of the critical line and the crossover exponent νz, for $d+z>d_{_{C}}$ by a dangerous irrelevant interaction. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.     

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.     

Quantum phase transition in an atomic bose gas with a feshbach resonance

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.     

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.     

Quantum phase transitions in the itinerant ferromagnet ZrZn2

We report a study of the ferromagnetism of ZrZn2, the most promising material to exhibit ferromagnetic quantum criticality, at low temperatures T as a function of pressure p. We find that the ordered ferromagnetic moment disappears discontinuously at p(c)=16.5 kbar. Thus a tricritical point separates a line of first order ferromagnetic transitions from second order (continuous) transitions at higher temperature. We also identify two lines of transitions of the magnetization isotherms up to 12 T in the p-T plane where the derivative of the magnetization changes rapidly. These quantum phase transitions (QPT) establish a high sensitivity to local minima in the free energy in ZrZn2, thus strongly suggesting that QPT in itinerant ferromagnets are always first order.     

Ising spin system with a rectangular distribution of internal energy parameters

The model of a spin system with internal degrees of freedom is solved for a rectangular distribution of the internal energy parameters. For simplicity, the interaction between the spin clusters is taken as the infinite range interaction. We obtain second and first order phase transitions with a tricritical point or a critical end point and an isolated critical point.     

Some aspects of the thermodynamic behaviour of ferroelastic and co-elastic phase transitions

Ferroelastic phase transitions and phase transitions involving coupling between the driving order parameter and elastic degrees of freedom (i.e. co-elastic phase transitions) follow empirically a Landau-type mean field behaviour over large temperature intervals. At temperatures close to the transition point the upper critical dimension is reduced to three if fluctuations are sufficiently constrained in reciprocal space. At low temperatures, the observed temperature independence of the order parameter in the saturation regime (S-regime) is correlated with the quantum limit of the dissipation-fluctuation theorem. The good agreement between experimental observations and the predictions of a Landau-type treatment of the excess Gibbs free energy even for large values of the order parameter leads to the conclusion that the convergency of the polynomial form of the Gibbs free energy is due to small energy coefficients rather than due to the order parameter being small.     

Theory of the vortex matter transformations in high-Tc superconductor YBCO

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transition line. The line, however, makes a wiggle near the experimentally claimed critical point at 12 T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy, and the specific heat discontinuities at melting compare well with experiments.     

Universal behaviors of mutual information in one-dimensional ${\sf J}_1-{\sf J}_2$ model

The critical behaviors of the entropy correlation effects in the one dimensional J₁-J₂ Heisenberg model are studied. It is shown that the mutual information or the correlation entropy captures the key features of information about critical fluctuations and can be used to quantify the quantum and finite-temperature phase transitions. At the critical point, the mutual information is power-law decay and the entanglement correlation length is infinite. While far away from the critical point, the mutual information is exponential decay and the entanglement correlation length is finite. A universal property of the mutual information is also found. Based on the critical behaviors of the mutual information, a new method to quantify the infinite order phase transition in the system is proposed.     

Phase structure of dynamical triangulation models in three dimensions

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling μ to the order of the vertices. Monte Carlo renormalization group and finite size scaling techniques are used to locate and characterize this line. Our results indicate that for μ < μ₁ ∼ −1.0 the model is always in a crumpled phase independent of the value of the curvature coupling. For μ < 0 the results are in agreement with an approximate mean field treatment. We find evidence that this line corresponds to first-order transitions extending to positive μ. However, the behavior appears to change for μ > μ₂ ∼ 2.0−4.0. The simplest scenario that is consistent with the data is the existence of a critical end point.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Quantum fluctuation driven first-order phase transition in weak ferromagnetic metals

In a local Fermi liquid (LFL), we show that there is a line of weak first-order phase transitions between the ferromagnetic and paramagnetic phases due to purely quantum fluctuations. We predict that an instability towards superconductivity is only possible in the ferromagnetic state. At T?=?0 we find a point on the phase diagram where all three phases meet and we call this a quantum triple point (QTP). A simple application of the Gibbs phase rule shows that only these three phases can meet at the QTP. This provides a natural explanation of the absence of superconductivity at this point coming from the paramagnetic side of the phase diagram, as observed in the recently discovered ferromagnetic superconductor, UGe ₂.     

Quantum effects on the competition between antiferromagnetism and superconductivity in heavy-fermion systems

We study a Ginzburg-Landau theory of two coupled fields describing superconductivity and antiferromagnetism in a metal. A coupling between the two-components superconductor and the antiferromagnetic (AF) field is included in the classical action. The classical results are improved calculating the quantum corrections to one-loop order with the method of the effective potential near the AF phase, but in the paramagnetic side. We discuss the influence of these corrections, including the possibility of fluctuation induced first order transitions. A scaling approach is used to obtain the critical and shift exponents at a quantum bicritical point.     

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.     

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.