Quantum Correlations Of One Dimension Heisenberg Spin Chain

Quantum correlations play key role in quantum information processing and quantum computation.Finding ways to manipulate and preserve sorts of quantum correlations in different physical systems is highly noted.Due to their good operability and convenient calculation,the quantum correlations in the Heisenberg spin chain have been studied extensively.Recently,multiple spin-exchange interactions play important roles in many real quasi-one-dimensional magnets,which lead extensive studies of the system with three-spin interactions.In consideration of the unavoidable system-environment interaction,the dynamics of different kinds of correlation has attracted much attention.This paper mainly investigates the following several respects.In Chapter 1,we introduce some sorts of the typical bipartite and tripartite quantum correlations,for instance,Concurrence,Discord,Geometric Discord,Tripartite Negativity,Tripartite Discord and Measurement-induced disturbance.Additionally,quantum phase transition phenomena and Heisenberg spin chain system are described in detail.In Chapter 2,we investigate the concurrence(C),geometric discord(GD)with reference to quantum phase transition in the XXZ spin chain with three-site interaction,and analyze the effects of two types of three-site interaction,magnetic field,anisotropy parameter,coupling constants J and temperature on concurrence,geometric discord.The result shows that concurrence,geometric discord can characterize the quantum phase transition phenomena.By increasing XZX+YZY interaction,concurrence and geometric discord could achieve the maximum even at high temperature.While the increase of XZY-YZX interaction has inhibitive effect on concurrence,and in some regions XZY-YZX interaction also has inhibitive effect on geometric discord,however,in some other regions,with the increase of XZY-YZX interaction,geometric discord could be enhanced to a steady value.Which implies that geometric discord describes the quantum correlation more comprehensively than concurrence.Additionally,entanglement can be enhanced by decreasing the magnetic field and the anisotropy parameter.The critical temperature is enhanced by increasing magnetic field and decreasing anisotropy parameter.In particular,the critical temperature increases significantly with the increase of the coupling constants J.Moreover,the value of geometric discord differed significantly from 0 even at the higher temperature while J is decreased.In addition,if the values of the other parameters are fixed,the concurrence,geometric discord reaches maximum value in the region of 0<B<5 and-1<Jz<10.In Chapter 3,Pairwise quantum discord and entanglement of the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated.Our study found that both entanglement and quantum discord could detect the quantum critical phenomena of this model.We were able to obtain a nonzero value of quantum discord even at high temperature with the increase of XZX+YZY or XZY-YZX three-site interaction,however,the cooperative effect of XZX+YZY and XZY-YZX interaction is more ideal.Furthermore,in contrast to XZY-YZX and XZX+YZY interactions,the cooperative effect of XZX+YZY and XZY-YZX three-site interaction is more efficient to enhance the maximum value of quantum discord.Likewise,the cooperative effect of XZX+YZY and XZY-YZX interactions are the most optimal to increase the range of magnetic field or anisotropy parameter where quantum discord maintains maximum values.In Chapter 4,The dynamics of the tripartite thermal entanglement measured by Negativity(N)and the tripartite quantum correlation described by Measurement-induced disturbance(MID)under Ornstein-Uhlenbeck noise are investigated.This study has found that the tripartite N and MID can be preserved more effective in the non-Markovian environment than in the short-time limit and the Markov limit cases.The short-time limit is a better approximation than the Markov limit.MID vanishes only in the asymptotic limit,while entanglement sudden death may occurs,and the decreasing duration of MID far outweighs entanglement.This implies that MID is more robust than Negativity.As the noise bandwidth increases,the disentanglement time and the decay time of MID are significantly shorter.The increase of XZX+YZY three-site interaction is more effective than XZY-YZX three-site interaction to enhance Negativity and MID as well as the disentanglement time.The magnetic field diminishes Negativity and MID,but has no significant influence on the decreasing durations of both Negativity and MID.In Chapter 5,Tripartite and bipartite quantum correlations in the three-qubit XXZ Heisenberg spin chain with two types of three-site interactions and an external magnetic field are investigated.We show that the increase of XZY-YZX interaction can enhance the robustness of both tripartite and bipartite correlations,whereas the increase of XZX+YZY interaction could improve the robustness of tripartite quantum correlations,but diminish the robustness of bipartite quantum correlations.Tripartite Measurement-induced disturbance is the most robust against temperature,and bipartite entanglement is the most fragile.Tripartite entanglement is even more robust than bipartite quantum discord when XZX+YZY or XZY-YZX interaction is relatively large.The cooperative effect of XZX+YZY and XZY-YZX interaction could induce bipartite entanglement even at high temperature.The cooperative effect of XZX+YZY and XZY-YZX interaction is the most optimal to improve the robustness of all quantum correlations when the magnetic field is negative.When the magnetic field is positive,the effective of XZY-YZX interaction alone is more ideal to preserve different quantum correlations.