Quantum Correlations And Phase Transitions In Low-dimensional Spin Chain

For the past few years,the quantum information science has made great progress in quantum storage,quantum computation,the precise manipulation of qubits,quantum communication,and quantum detection.In many simulative systems of quantum information,the system of quantum spins can supply a large number of qubits resource,have the expandability and the high integration,so it provides an ideal platform for the research on quantum fundamental theory and related experimental techniques.In this thesis,based on the one-dimensional spin-chain model,we study the critical behaviours and the characteristics of dynamic evolution of the quantum entanglement,quantum discord,quantum coherence,and quantum speed limit(QSL)time.Simultaneously,we also investigate the topological quantum phase transitions(TQPTs)of the extended XY spin-chain,and the relationship between the quantum Fisher information(QFI),quantum coherence and the TQPTs,respectively.The main research contents and results are as follows:We investigate the prominent impacts of the system–environment coupling situations on the evolution of entanglement,quantum discord and coherence for a three-qubit system coupled to an XY spin-chain environment.Quantum entanglement,quantum discord and coherence are frozen for the three-qubit system coupled to an XY spin-chain environment as the system–environment coupling satisfies certain conditions,then,the steady quantum resources can be obtained in quantum many-body environment.We also compare the dynamics of quantum coherence with that of the entanglement and the quantum discord.The analysis shows no hierarchical relationship among them.Lastly,the initial states of three-qubit system,the strength of magnetic field,anisotropic parameter,and the scale of the environment strongly affect coherence evolution.We study the QSL time of a qubits system coupled to the spin-chain model with the Dzyaloshinsky-Moriya(DM)interaction or the three-spin interaction.The qubit systems are assumed to the Bell state and Werner-like state.We find that the DM interaction and the three-spin interaction can effectively manipulate the critical value of the QSL time.They make the QSL time mark more clearly the quantum phase transition of the onedimensional spin-chain models.Especially the XX model,the DM interaction and the three-spin interaction make it possible for us to witness the quantum phase transition by the local anomalous enhancement of the QSL time near the critical point.In addition,the dynamical evolution of the QSL time presents a periodic behavior in quantum-critical environment,whereas the three-spin interaction and external magnetic field can destroy this periodicity.Based on the energy spectra of the ground state and the trajectories of winding vectors in a two-dimensional plane,we investigate the topological characteristics of the extended XY spin-chain.We also study the relationship between the QFI of spin-pairs and the TQPTs of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins,the transverse magnetic field,and the three-spin interaction.We find that the first derivative of QFI can correctly characterize the TQPTs at the absolute zero temperature.Meanwhile,the impacts of the finite temperatures and the site distance of spin-pairs on the critical behaviors of the QFI are studied.It is found that the first derivative of QFI for the nearest-neighbor or the long-distance spin-pairs,can only correctly characterize the critical points of the TQPTs at sufficiently low temperature.Remarkably,when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters,the QFI itself can characterize the partial TQPTs at the absolute zero temperature.We study the quantum criticality of single-and two-spin coherence,based on the quantum skew information,in the extended XY spin-chain,and analyze the impact of different driving parameters,finite temperatures and site distance of spin-pairs on their critical behaviors.We find that the first-order derivative of quantum coherence can correctly mark the topological phase transition points,but the thermal fluctuations strongly affect the accuracy of detection for critical points.For the case of long-distance spin-pairs,we find the first-order derivative of two-spin coherence can also correctly mark the phase transition points at the absolute zero temperature.Moreover,the quantum coherence itself under absolute zero temperature can also signal the topological phase transition points by a local extremum in several certain situations.