| Quantum correlation has stimulated more and more attention because its nonclassical correlation can be used as an vital resource in quantum information processing.Quantum spin system has rich properties of entanglement in condensed matter physics.There are two main directions of the research of spin system.One is to investigate the relation between quantum correlation(or quantum entanglement)at the low or absolute zero temperature and quantum phase transition in these systems,and the other one is to disclose the relation between the thermal fluctuation caused by the finite temperature and the quantum correlation.We mainly study the properties of multipartite quantum correlation measurement in one dimensional solid spin chain system.By means of the quantum renormalization group,we studied the relationship between the ground state correlation and the quantum phase transition in different spin systems.The results are as follows:(1)We analytically investigate the thermal entanglement of three-mixed-spin(1/2,1,1/2)XXZ model with the DM interaction under an external magnetic field B.Two different cases are considered:one subsystem(1/2,1/2)consists of two spin-1/2 fermions,and the other subsystem(1/2,1)contains a spin-1/2 fermion and a spin-1 boson.It is shown that the DM interaction parameter D,the external magnetic field strength B and coupling constant J have different effects on quantum entanglement of Fermi and mixed Fermi-Bose systems.All of the factors mentioned above can be utilized to control entanglement switch of any two particles in mixed spins model.It can shed new light on the interplay between the quantum nature of the system and its macroscopic state variables,and provide a theoretical basis for the control quantum entanglement and the realization of quantum communication.(2)The effect of Dzyaloshinskii-Moriya interaction and anisotropy on the?-tangle and quantum phase transition(QPT)by employing the QRG method in the one-dimensional anisotropic XY model is investigated.In our model the anisotropy and DM interaction parameters can influence the phase diagrams.While the anisotropy suppresses the entanglement due to favoring of the alignment of spins,the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations.When the value of DM interaction is certain,the ?-tangle develops into two different values which separate the system into two phases i.e.Spin-fluid phase and the Neel phase with the number of QRG iterations increased.Meanwhile,the?-tangle decreases slowly as the sites of the chain became larger,but the ?-tangle tends to be a fixed value finally.Additionally,it exhibits a maximum for the next-nearest-neighbor entanglement at the critical point in our model which is different from the situation of two-body system.Then,the nonanalytic and scaling behavior of ?-tangle have also been analyzed in detail and this phenomenon indicates that the behavior of the entanglement can perfectly help one to observe the quantum critical properties of the model.(3)The effect of external magnet field g on the relationship among the quantum discord,Bell non-locality and quantum phase transition(QPT)by employing QRG method in the one-dimensional transverse Ising model is investigated.In our model external magnet field g can influence the phase diagrams.The results have shown that both the two quantum correlation measures can develop two saturated values,which are associated with two distinct phases:long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing.Additionally,quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block,but for nearest-neighbor blocks in the long-ranged ordered Ising phase.However the block-block correlation in the paramagnetic phase is not strong enough to violate the Bell-CHSH inequality as the size of system becomes large.Furthermore,when the system violates the CHSH inequality,i.e.,satisfies quantum non-locality,it needs to be entangled.On the other way,if the system obeys the CHSH inequality,it may be entangled or not.To gain further insight,the nonanalytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.(4)We study the relation among quantum coherence,uncertainty,steerability of quantum coherence based on skew information and quantum phase transition in the spin model by employing quantum renormalization-group method.Interestingly,the results show that the value of the local quantum uncertainty is equal to the local quantum coherence corresponding to local observable ?z in XXZ model,and this proposition can be generalized to a multipartite system.Therefore,one can directly achieve quantum correlation measured by local quantum uncertainty and coherence by choosing different local observables ?z,corresponding to the XXZ model.Meanwhile,we investigate non-local advantage of quantum coherence in XXZ model systematically,and the results reveals that no matter what the value of anisotropy is and what times the QRG iterations are carried out,the quantum coherence of the state of subsystem can't be steerable,which can also be suitable for two sites of a block and block-block steerability of local quantum coherence in XXZ model.Additionally,after several iterations,the quantum coherence and uncertainty measure can develop two saturated values,which are associated with two different phases:spin-fluid phase and the Neel phase.To gain further insight,the nonanalytic and scaling behaviors of non-local advantage of quantum coherence have been analyzed in detail.We can find that the quantum critical properties were connected with the behavior of the non-local advantage of quantum coherence. |
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