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.     

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.     

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.     

Pairwise Entanglement and Quantum Phase Transitions in Spin Systems

We examine several well-known quantum spin models and categorize the behaviour of pairwise entanglement at quantum phase transitions. A unitied picture on the connection between the entanglement and quantum phase transition in spin systems is presented.     

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.     

具有三自旋相互作用XX模型纠缠特性研究

利用Concurrence判据,研究了具有三自旋相互作用的XX模型的纠缠特性;分别在铁磁和反铁磁模型中研究了三自旋相互作用J_2和温度T对两自旋纠缠度的影响.结果表明,三自旋相互作用J_2提高系统的两体纠缠度,但是提高程度会因最近邻自旋间发生铁磁、反铁磁相互作用而有所差异;并且J_2影响两自旋系统纠缠消失的临界温度T_C,T_C会随J_2的增大而减小.系统温度T影响两体纠缠度,随着温度的降低,纠缠度会得到提高.此外,分别在系统本征态和基态中研究了两自旋的纠缠度,求出了系统发生量子相变的量子临界点.     

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.     

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.     

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 phase transitions and bipartite entanglement

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.     

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.     

三量子位和四量子位Heisenberg XY链中的纠缠与自旋压缩(英文)

研究了三量子位和四量子位Heisenberg XY链中的基态纠缠与自旋压缩,给出了纠缠C和自旋压缩参数ξ2的解析表达式.结果表明,当外部磁场B大于某一临界值Bc时,纠缠与自旋压缩等价,即纠缠意味着自旋压缩,反之亦然.对三量子位情形,Bc=J[(4-3γ2)1/2-1];对四量子位情形,Bc可以通过数值方法进行求解.     

具有三角自旋环的伊辛-海森伯链的热纠缠

研究了具有三角自旋环的伊辛-海森伯链在磁场作用下的热纠缠性质.分别讨论了三角自旋环中自旋1/2粒子间相互作用的三种情形,即XXX,XXZ和XY Z海森伯模型.利用转移矩阵方法,数值计算了具有三角自旋环的伊辛-海森伯链的配对纠缠度.计算结果表明,外加磁场强度和温度对系统处于上述三种海森伯模型的热纠缠性质均有重要影响.给出了系统在不同的海森伯模型下,纠缠消失对应的临界温度随磁场强度的变化图,由此可以得到系统存在配对纠缠的参数区域,同时发现在特定的参数区域存在纠缠恢复现象.因此适当调节温度和磁场强度,可以有效调控具有三角自旋环的伊辛-海森伯链热纠缠性质.     

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.     

{Cu3}单分子磁体在磁场中的热纠缠

本文研究单分子磁体Na₉[Cu₃Na₃(H₂O)₉ (α-AsW₉O₃₃)₂]·26H₂O中三角自旋 环在磁场作用下的热纠缠性质, 利用数值计算求出任意两个Cu²⁺离子量子比特之间的配对纠缠度, 分别记为C₁₂, C₂₃和C₁₃. 研究结果表明, 磁场的方向和大小以及温度对配对纠缠度具有重要影响, 而且参数的变化对C₁₂, C₂₃和C₁₃的影响也是各不相同. 给出外加三个不同方向的磁场时, 配对纠缠度C₁₂, C₂₃和C₁₃各自对应的临界温度T_c随磁场强度的变化图, 由此可以得到单分子磁体三角自旋环中存在纠缠态的参数范围. 通过选择适当的磁场方向和大小以及温度等实验参数, 可以有效地调节和提高单分子磁体中的配对纠缠度. 关键词： 配对纠缠 单分子磁体 三角自旋环     

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 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.     

Thermal entanglement in a triple quantum dot system

We present studies of thermal entanglement of a three-spin system in triangular symmetry. Spin correlations are described within an effective Heisenberg Hamiltonian, derived from the Hubbard Hamiltonian, with super-exchange couplings modulated by an effective electric field. Additionally a homogenous magnetic field is applied to completely break the degeneracy of the system. We show that entanglement is generated in the subspace of doublet states with different pairwise spin correlations for the ground and excited states. For the doublets with the same spin orientation one can observe nonmonotonic temperature dependence of entanglement due to competition between entanglement encoded in the ground state and the excited state. The mixing of the states with an opposite spin orientation or with quadruplets (unentangled states) always monotonically destroys entanglement. Pairwise entanglement is quantified using concurrence for which analytical formulae are derived in various thermal mixing scenarios. The electric field plays a specific role – it breaks the symmetry of the system and changes spin correlations. Rotating the electric field can create maximally entangled qubit pairs together with a separate spin (monogamy) that survives in a relatively wide temperature range providing robust pairwise entanglement generation at elevated temperatures.     

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.     

Local Unitary Invariant Spin-Squeezing in Multiqubit States

We investiage Local Unitary Invariant Spin Squeezing (LUISS) in symmetric and non-symmetric multiqubit states. On developing an operational procedure to evaluate Local Unitary Invariant Spin Squeezing parameters, we explicitly evaluate these parameters for pure as well as mixed non-symmetric multiqubit states. We show that the existence of local unitary invariant version of Kitegawa-Ueda spin squeezing may not witness pairwise entanglement whereas the local unitary invariant analogue of Wineland spin squeezing necessarily implies pairwise entanglement.