Quantum Phase Transition and Thermal Entanglement in the Isotropic XXX Model

We investigate the quantum phase transition (QPT) and the pairwise thermal entanglement in the three-qubit Heisenberg XXX chain with Dzyaloshinskii--Moriya (DM) interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a QPT. At a given temperature, the entanglement undergoes two sudden changes (platform-like behavior) as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.     

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.     

Quantum Phase Transition and Thermal Entanglement in the Ising Model with Dzyaloshinskii-Moriya Interaction in an Inhomogeneous Magnetic Field

We investigate the quantum phase transition (QPT) and thermal entanglement in the two-qubit Ising model in an inhomogeneous magnetic field, and the DM interaction between the two lattices is considered. The results show the QPT highly relates to the magnetic intensity B and DM parameter D, by controlling the DM interaction D and external magnetic B we can change the positions of QPT points and the level spacing. Moreover, the QPT is closely related to thermal entanglement, when the QPT happens the ground state always changes between entanglement state and disentanglement state. The thermal entanglement highly depends on the system’s temperature T, DM intensity D and external magnetic field B. When T is lower, the entanglement can exhibit a platform-like region. By modulating the parameters D and B, the entanglement can be controlled and the entanglement switch can be realized.     

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.     

Quantum Coherence and Correlation in Spin Models with Dzyaloshinskii-Moriya Interaction

We study quantum coherence and quantum correlation for detecting quantum phase transition (QPT) by means of quantum renormalization group (QRG) in various spin chain models with Dzyaloshinskii-Moriya (DM) interaction, including XXZ model with DM interaction, Ising model with DM interaction and XY model with DM interaction. It is found that through enough QRG iterations, l ₁ norm quantum coherence and one-norm geometric quantum discord can effectively characterize QPT. We also discuss the effect of DM interaction and anisotropy on quantum coherence and quantum correlation.     

Robustness of entanglement as a signature of quantum phase transitions

We investigate the critical behavior of pairwise entanglement at quantum phase transitions (QPT) in several exactly solvable spin models with noise in system control parameters. We show that the exact critical behavior will change due to noise. When the noise is not too large, pairwise entanglement is robust as a signature of QPT in some spin models.     

Entanglement dynamics of three-qubit coupled to an XY spin chain at finite temperature with three-site interaction

The entanglement dynamics of three-qubit states under an XY spin chain at finite temperature with three-site interaction is investigated. It is shown that the three-site interaction does not affect the behavior of quantum phase transition (QPT) induced by the external magnetic field and does not induce new critical regions in the XY model. In addition, concerned with the effect of the three-site interaction on the entanglement evolution, we find the three-site interaction can not only enhance but also suppress the decay of the entanglement between the three-qubit system, which depends on the initial states of the system and the parameters related with the environmental spin chain.     

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.     

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.     

Negativity and Quantum Phase Transition in the Spin Model Using the Quantum Renormalization-group Method

In this paper, we study the anisotropy parameter and Dzyaloshinskii-Moriya (DM) interaction on negativity and quantum phase transition (QPT) by using the quantum renormalization-group (QRG) method in the spin model. In our model, the anisotropy parameter and DM interaction can influence the phase diagrams. Negativity can develop two different values which separated two phases i.e. Spin-fluid phase and the Néel phase with the number of QRG iterations increased, and can obviously exhibit QPT at the critical point. Then, we find that negativity of particles 1, 3 throughout is less than negativity of particles 1, 2 or particles 2, 3. Because of information between the three particle distributions, please see the conclusion. We find that the negativity difference value (S) can also clearly detect QPT at the critical point. Most importantly, the maximum S _max become more and more close to the critical point. So S _max can be used as a criterion of the quantum phase transition occurrence when the spin chain is infinity (N → ∞).     

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.     

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.     

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.     

Quantum Phase Transition and Local Entanglement in Extended Hubbard Model on Anisotropic Triangular Lattices

Using a mean-field theory based upon Hartree-Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.     

Quantum Dynamics of Entanglement and Single Excitation Transfer in LH1-RC-Type Trimer

In this paper, we study quantum dynamics of entanglement and single excitation transfer (SET) in an LH1-RC-type trimer which can describe a basic unit cell in the LH1-RC complex in the photosynthetic process. It is shown that there exists a sudden change of entanglement at the critic point of quantum phase transition (QPT) of the system at low temperatures, the entanglement sudden change caused by the QPT is suppressed at higher temperatures. We investigate the influence of environment on entanglement and SET. We show the generation of the dephasing-assisted entanglement between a donor and an acceptor and the existence of the steady-state entanglement, and demonstrate the entanglement transfer from donor-donor entanglement to donor-acceptor entanglement in the dynamic evolution. We reveal the close relation between the SET probability and donor-acceptor entanglement. Especially, we find that the SET probability is proportional to the amount of donor-acceptor entanglement under certain conditions.     

Quantum Dynamics of Entanglement and Single Excitation Transfer in LH1-RC-Type Trimer

In this paper,we study quantum dynamics of entanglement and single excitation transfer(SET) in an LH1-RC-type trimer which can describe a basic unit cell in the LH1-RC complex in the photosynthetic process.It is shown that there exists a sudden change of entanglement at the critic point of quantum phase transition(QPT) of the system at low temperatures,the entanglement sudden change caused by the QPT is suppressed at higher temperatures.We investigate the influence of environment on entanglement and SET.We show the generation of the dephasing-assisted entanglement between a donor and an acceptor and the existence of the steady-state entanglement,and demonstrate the entanglement transfer from donor-donor entanglement to donor-acceptor entanglement in the dynamic evolution.We reveal the close relation between the SET probability and donor-acceptor entanglement.Especially,we find that the SET probability is proportional to the amount of donor-acceptor entanglement under certain conditions.     

具有Dzyaloshinskii-Moriya相互作用的三量子比特海森伯模型中的对纠缠

研究了一维三量子比特海森伯模型中的对纠缠的提高和控制问题,在该系统中引入了Dzyaloshinskii-Moriya（DM)相互作用,通过求解共生来计算两量子比特之间的热纠缠,结果表明：对于XXX模型,引入DM相互作用D,可以诱导铁磁和反铁磁自旋链产生热纠缠,尽管它们产生热纠缠所需的D值大小不同.对于XXZ模型,引入DM相互作用后,可以使原本不存在热纠缠的反铁磁自旋链产生纠缠,而且对于铁磁和反铁磁这两种XXZ自旋链,DM相互作用和各向异 关键词： 纠缠 XXX模型')" href="#">XXX模型 XXZ模型')" href="#">XXZ模型 Dzyaloshinskii-Moriya相互作用     

Ground-State and Thermal Entanglement in Three-Spin Heisenberg-XXZ Chain with Three-Spin Interaction

The entanglement properties of a three-spin X X Z Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at A = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J/T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.     

Ground-State and Thermal Entanglement in Three-Spin Heisenberg-XXZ Chain with Three-Spin Interaction

The entanglement properties of a three-spin X X Z Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at △ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J/T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.     

Entanglement in One-Dimensional Random XY Spin Chain with Dzyaloshinskii--Moriya Interaction

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii-Moriya （DM） interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. （i） For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. （ii） For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings （or magnetic field） play competing roles in enhancing quantum entanglement.