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.     

Quantum Phase Transitions,Entanglement Spectrum,and Schmidt Gap in Bond-Alternative S=1 Antiferromagnetic Chain

Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation （iTEBD） method. The quantum phase transition （QPT） from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around rc ~- 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetie correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.     

Entanglement spectrum and magnetization plateaus in an S = 1 bond-alternative Heisenberg chain with single-ion anisotropy and magnetic field

Entanglement spectrum and quantum phase transitions (QPTs) in S = 1 bond-alternative antiferromagnetic Heisenberg chain with single-ion anisotropy and magnetic field are investigated by the infinite time-evolving block decimation (iTEBD) method. The combined effects of the single-ion anisotropy and magnetic field have been discussed, and a rich ground-state phase diagram is obtained. We find that the single-ion anisotropy is advantageous to the stability of the 1/2 magnetization plateau. Both entanglement entropy and entanglement spectrum, as two model-independent measures, are capable of describing all the QPTs. Especially, doubly degenerate entanglement spectrum on even bond is observed in the 1/2 plateau phase. Besides constant spontaneous magnetization, three magnetization plateaus (M ^z = 0, 1/2, and 1) are found to have constant entanglement entropy, entanglement spectrum, and nearest-neighbor correlation. In addition, all the QPTs in such a model have been determined to belong to the second-order category.     

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field *

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglemententropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field .The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum hase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge $c=1$ is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.     

Quantum phase transition and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a double-well potential

We investigate the quantum phase transition (QPT) and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a symmetric double well under the mean-field approximation. We find the system undergoes a new QPT towards phase-locking state when atom-pair tunnelling is strong enough, and the critical point of self-trapping QPT is shifted by atom-pair tunnelling. As for the dynamics, the system displays localized dynamical behaviour: phase-locking motion and self-trapping motion. We further study the correlation between this localized dynamics and QPT, and find that the area of the localized trajectories in the phase space can serve as an order parameter for both QPTs. The critical exponent of this order parameter is also discussed.     

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

Through the Jordan-Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called ``spin waves', which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.     

Critical entanglement and geometric phase of a two-qubitmodel with Dzyaloshinski--Moriya anisotropic interaction

We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski--Moriya (DM) anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition (QPT). It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.     

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.     

Bell-CHSH function approach to quantum phase transitions in matrix product systems

Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) function. In this work, we extend the study of the Bell-CHSH function (BCF) to QPTs in matrix product systems (MPSs). In these kinds of QPTs, the ground-state energy remains analytical in the vicinity of the QPT points, and they are usually called MPS-QPTs. For several typical models, our results show that the BCF can signal MPS-QPTs very well. In addition, we find the BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.     

182Os核yrast带结构SU(3)→U(5)→SU(3)形状相变的有序性研究

对于发生在同一个原子核中的转动诱导发生基准态结构的量子相变,可以理解为一种从高有序激发模式向着低有序激发模式的演化：被布居到高角动量态的高有序激发核,以E2跃迁的方式先行退耦到yrast带,再退耦到共存区(或临界点)时释放了有序的结构能,诱发价核子对耦合强度改变,重新组合出低有序的激发模式基准态,实现了基准态结构的过渡.对核量子相变的这种描述,与朗道经典热相变理论之间有了某些相似的术语和物理内涵.本文把这种理解推广到了相继的二次相变中.以¹⁸²Os 核为例作了说明,并展 关键词： 量子相变 基态结构演化 F_max方案')" href="#">微观sdIBM-F_max方案 182Os核')" href="#">¹⁸²Os核     

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.     

Multipartite entanglement signature of quantum phase transitions

We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.     

Grüneisen ratio quest for self-duality of quantum criticality in a spin-1/2 XY chain with Dzyaloshinskii–Moriya interaction

The quantum phase transition(QPT) and quantum criticality of an anisotropic spin-1/2 XY chain under the interplay of magnetic field and Dzyaloshinskii–Moriya(DM) interaction, which is interpreted as an electric field, are investigated, wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order. It is shown that the thermal Drude weight is a good quantity to characterize the gapped(D_(th) = 0) and gapless(D_(th) 0) ground states. The continuous QPT is marked by a quantum critical point(QCP) associated with entropy accumulation, which is manifested by a characteristic Güneisen ratio(GR) with or without selfduality symmetry. It is shown that at a self-dual QCP, the GR keeps a finite value as T→0,while at a general QCP without self-duality symmetry, it displays a power-law temperature dependent divergence: Γ(T,r_c)～±T~(-1),which provides a novel thermodynamic means for probing QPT.     

Quantum phase transitions about parity breaking in matrix product systems

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.     

Entanglement and quantum phase transition in the Heisenberg-Ising model

We use the quantum renormalization-group(QRG) method to study the entanglement and quantum phase transition(QPT) in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.(N.Y.) 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.     

Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.     

Quantum Phase Transitions in Matrix Product States

We present a new general and much simpler scheme to construct various quantum phase transitions （Q, PTs） in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state （MPS） OPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of Q, PT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.     

Quantum phase transitions about parity breaking in matrix product systems

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.