The dynamics of a central spin in quantum Heisenberg XY model

In the thermodynamic limit, we present an exact calculation of the time dynamics of a central spin coupling with its environment at finite temperatures. The interactions belong to the Heisenberg XY type. The case of an environment with finite number of spins is also discussed. To get the reduced density matrix, we use a novel operator technique which is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. The expectation value of the central spin and the von Neumann entropy are obtained.     

非匀强磁场中双量子位Heisenberg XY链的基态纠缠和热纠缠(英文)

研究了非匀强磁场中各向异性Heisenberg XY链的基态纠缠和热纠缠.结果表明对双量子位情形,纠缠与格点间耦合常数J、外部磁场B、各向异性参数γ和b的正负无关.对绝对零度情形,我们给出了纠缠C的解析表达式,并指出临界磁场Bc随磁场各向异性参数b的增大而增大.对有限温度情形,我们给出了γ=0时C的解析表达式和γ≠0时的数值模拟结果,结果发现引进非匀强磁场可以使纠缠在某些区域明显增大;同时我们还指出当γ=0时,纠缠存在的临界温度Tc仅是b的增函数,而当γ≠0时,它却由B和b共同决定.     

Quantum correlation dynamics in a two-qubit Heisenberg XY Z model with decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XY Z model under decoherence is investigated by making use of concurrence C and quantum discord(QD).Firstly,we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented:there is an entanglement intermittently sudden death phenomenon in the concurrence but not in the QD,which is valid for all the initial states of this system.Also,the interval time of entanglement sudden death is found to be strongly dependent on the initial states,the inhomogeneous magnetic field b and the anisotropic parameter ?.Then,it implies that the steady concurrence and QD can be obtained in the long-time limit,which means that the environmental decoherence cannot entirely destroy the quantum correlation,the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot.In addition,based on the analysis of the steady concurrence and QD with t →∞,we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and △,whereas the parameter b is independent of the steady concurrence and QD.     

Evolution of entanglement in the Heisenberg XY model: the Yangian algebra method

We construct transition operators in terms of generators for Yangian and act with them on the entangled state of the Heisenberg XY model. Different parameter values of the transition operators lead to different evolutions of the entanglement degree of the final states. It is interesting and worth noting that for some special parameters in the transition operators, our calculation is in good agreement with the experiment. This result sheds a new light on the physics of Y(sl(2)) in quantum information.     

Observation of geometric phase in a dispersively coupled resonator-qutrit system

We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit's ground state and first-excited state along different circular trajectories in phase space. We identify the resonator's phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit π-phase gate with a process fidelity of 0.851 ± 0.001.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

Quantum Correlations in Heisenberg XY Chain

Quantum correlations measured by quantum discord (QD), measurement-induced distance (MID), and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated. The effects of DM interaction and anisotropic on the three correlations are considered. Characteristics of various correlation measures for the two-qubit states are compared. The increasing D z increases QD, MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD. The three quantum correlations are always existent at very high temperature. MID is always larger than QD, but there is no definite ordering between QD and GMQD.     

Striped phase in a quantum XY model with ring exchange

We present quantum Monte Carlo results for a square-lattice S=1/2 XY model with a standard nearest-neighbor coupling J and a four-spin ring exchange term K. Increasing K/J, we find that the ground state spin stiffness vanishes at a critical point at which a spin gap opens and a striped bond-plaquette order emerges. At still higher K/J, this phase becomes unstable and the system develops a staggered magnetization. We discuss the quantum phase transitions between these phases.     

Thermodynamic study of 3D XY model and Heisenberg model by analytical method

With Variational-Cumulant Expansion method, the specific heat and spontaneous magnetization of 3D classical XY model and Heisenberg model are calculated respectively up to the 5th and 4th order. The variational parameter is determined both by the Main Value method and by the accumulation point method. It is shown that the specific heat curve and the magnetization curve obtained by the accumulation point method are in better agreement with the MC results. The critical point T _c and critical exponent β* are also calculated for the XY model.     

Scaling of geometric phases close to the quantum phase transition in the XY spin chain

We show that the geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.     

Interplay between anisotropic exchange coupling and the swap operation in the two-qubit Heisenberg XY model

In this Letter we investigate the interplay between Zeeman splitting and the exchange-induced swap operation in Heisenberg XY model. It is shown that the anisotropic exchange coupling can rule out the swap action even if the magnetic field is homogeneous. The time-evolution of entanglement is also studied and we find that the degree of entanglement of the two spins is suppressed in the presence of inhomogeneous magnetic fields.     

外磁场下XY模型中两量子位热纠缠的性质及其调控研究

在海森堡XY模型中,为了统一研究均匀磁场和非均匀磁场对系统热纠缠的影响,在两个量子位分别施加独立可控的外磁场(B+b)和(B-b). 发现在均匀磁场和低温条件下的纠缠度有一个稳定的平台区并发生纠缠突变. 控制磁场不均匀度b和选择合适的材料就可以获得最有利的纠缠,并大大提高系统退纠缠的临界温度Tc. 调节磁场的B值,可以在更宽的温度范围内实现此体系的纠缠开关.     

Measurement-induced disturbance in Heisenberg XY spin model with Dzialoshinskii–Moriya interaction under intrinsic decoherence

Quantum correlations measured by measurement-induced disturbance （MID） in a two-qubit Heisenberg XY spin model with Dzialoshinskii-Moriya （DM） interaction under intrinsic decoherence are investigated. MID is studied un-der various circumstances and the influences of the external dependencies on the final quantum state which has stable MID are discussed. Two kinds of initial quantum states are considered as well as different conclusions. MID appears to decay periodically during the processing of intrinsic decoherence; both DM interaction and intrinsic decoherence have a negative impact on the correlations. The MID of the stable state depends on several factors, except the parameter of the intrinsic decoherence. Moreover, we find a special initial state that is able to maintain the maximum quantum correlations during the processing of intrinsic decoherence.     

The phase transition in the fully frustrated XY model as a percolation problem

The fully frustrated planar rotator and fully frustrated XY models in two dimensions have two phase transitions: one of the Berezinskii–Kosterlitz–Thouless type and other in the Ising universality class. We use Monte Carlo simulation to study both models. We fix our attention in the Ising-like transition, which we show can be understood as a percolation transition. We obtain the critical temperature as well as the critical exponents of the mean cluster size, γ, and Fisher's exponent τ. The critical temperature agree very well with other calculations. We found that the critical exponents are smaller than in the pure two-dimensional percolation case. We interpret this as due to the long-range interaction between vortex and antivortex.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.