Studies Of Quantum Correlation And Quantum Phase Transition In Spin-Chain And Open Systems

Quantum information science is an an interdisciplinary research area which evolves quan-turn mechanics and information science.Quantum information theory has many advantages over classical information theory because of the quantum mechanics,especially in information search and communication security.In such an unprecedented information age,the rapid development of the Internet,big data and artificial intelligence are all depending on the speed of information processing and the security of information exchange.Classical information theory is becoming more and more stretched in this conditions.It is the development of quantum information the-ory which gives the future of information science more possibilities.Various quantum algorithms based on quantum fast Fourier transform greatly break through the limitations of classical algo-rithms in information search and large number decomposition tasks,while no-cloning theorem of quantum states gives quantum key distribution and secure communication the absolute security theoretically.This young area is considered to be the foundation for the next generation of com-puter systems,and has attracted widespread attentions.At the same time,quantum information science also injects new blood into other branches of physics.Experiments of quantum informa-tion motivate the development of optics and atomic physics,while theories of quantum information provide new research ideas and methods for the condensed-matter physics.The difference between quantum information and classical information comes from the non-classical correlation of quan-turn systems,that is,quantum correlation,which is an indispensable resource for realizing various quantum information tasks.Quantum entanglement,quantum discord,and quantum coherence are regarded as the physical resources required for quantum information tasks and have received numerous researches.On the one hand,quantum correlations make it possible to study quantum phase transitions and critical behaviors regardless of the traditional order parameters and symme-try broken,and thus become a research hotspot in the condensed-matter physics.In recent years,many physical quantities from quantum information science,such as trace distance,fidelity,quan-turn entanglement,and quantum coherence,have successfully been used to characterize quantum phase transitions and critical behaviors in many-body systems.On the other hand,quantum corre-lations are very fragile and easily destroyed by decoherent phenomenon induced from environment noise.This is one of the obstacles that must be overcome to achieve the real world quantum com-puting.Therefore,the study of quantum correlations and control of environmental decoherence in the dynamics of open quantum systems are of practical significance.In this paper,we first apply the renormalization group method to study the quantum cor-relations and quantum phase transitions in many-body systems.We make use of the real space renormalization group method to study the relative entropy of coherence and violation of Bell in-equality in the XY spin chain with Dzyaloshinskii-Moriya(DM)interaction and find that the first derivatives of the renormalized quantum coherence as well as Bell inequality exhibit singularity near the critical point of the quantum phase transition.We explore the finite-size scaling behav-iors of the first derivatives of the quantum coherence at the critical point of the quantum phase transition,and obtain several universal finite-size scaling laws.The critical exponents of these universal finite-size scaling laws are directly related to the correlation length exponent around the critical region.Next,we use the density matrix renormalization group(DMRG)method to study the behavior of multipartite entanglement near the quantum phase transition point of the anisotropic XYZ spin chain,including the anisotropic XYZ with nearest-neighbor interaction and next-nearest-neighbor interaction.Multipartite entanglement changes dramatically near the critical region and the residual-to-global entanglement ratio reaches its maximum at the critical point of the quantum phase transition.These results indicate that multipartite entanglement as well as the residual-to-global entanglement ratio can serve as good indicators to detect a quantum phase transition in this model.We also demonstrate a linear relation between the next-nearest-neighbor interaction strength and the critical magnetic field for an XYZ spin chain by using multipartite entanglement and quantum coherence.Another topic of this paper is to study the dynamical properties of quantum correlations.We study the decoherence procedure and entanglement generation for infinitely connected Ising chain in the dynamical quantum phase transition region by making use of the matrix-product state alone with the time-dependent variational principle.By calculating the evolution of multipartite entan-glement and relative entropy of coherence,we find that the quantum coherence reaches its local minimum near the critical time of the dynamical quantum phase transition while the multipartite entanglement increases steeply,which means the system undergoes a recovery of coherence as well as an acceleration of creating entanglement at the same time in the vicinity of a dynamical quantum phase transition.Furthermore,we investigate the depends of decoherence and entangle-ment generation on the strength of the transverse magnetic field and obtain several power-law rela-tions.These dynamical properties are important and useful in the preparation of highly-entangled states with strong coherence which may provide the possibility of completing complex quantum tasks.On the other hand,we use the hierarchical equations of motion method to study the dynamic behaviors of quantum memory-assisted entropy uncertainty relation and quantum speed limit in a quantum dissipative system.It is demonstrated that the weak measurement and measurement reversal can suppress the entropic uncertainty during the evolution of the system,and we find a periodical crossover of the quantum speed limit time for different weak measurement strengths,which disappears when increasing the coupling strength.Similar influence of the weak measure-ment on uncertainty relations is then explored at the finite temperature.We also consider the effect of the counter-rotating-wave term and show that the rotating-wave approximation is an applicable approximation when studying quantum speed limit time but not appropriate when investigating the quantum-memory-assisted entropic uncertainty relation.