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Entanglement And Quantum Phase Transition In The One-dimensional Anisotropic XY Model

Posted on:2011-01-31Degree:MasterType:Thesis
Country:ChinaCandidate:S X LiuFull Text:PDF
GTID:2120360305968565Subject:Condensed matter physics
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Quantum entanglement, as one of the most intriguing features of quantum theory, has attracted much attention in recent years, mostly because its non-classical correlations is regarded as a valuable resource in quantum-communication and quantum-information processing. It plays a key role in a quantum phase transition, and attracts much attention. In this thesis,.we study the thermal entanglement and the entanglement at absolute zero temperature in the one-dimensional anisotropic XY model. The main results are as follows:The pairwise entanglement in (1/2,3/2) mixed-spins and(s=1)XY systems are investigated by means of the concept of negativity. At the different temperatures, we found that the entanglement of the large spin and mixed-spins to reach a stable value due to the DM interaction. Exchange-coupling interaction between the spins is helpful to the strength of the entanglement. When the exchange-coupling interaction is smaller, we can enlarge the DM interaction to raise the entanglement while for the DM interaction is smaller, we can increase the exchange-coupling interaction. The higher the temperature is, the smaller the entanglement is. To enhance the value of thermal entanglement, we need a stronger DM interaction. Given the same conditions, the large spin (s=1) entanglement between two particles is more powerful than that of the mixed-spins.The critical behavior of the anisotropic(s= 1/2)XY model by the method of quantum renormalization group is studied. We found that the concurrence between two blocks can be regarded as an order parameter. Using the renormalization equation, we obtained the evolution of entanglement, non-analytic behaviors and scaling behaviors between the two blocks. As the size of the system becomes larger, the first derivative of the concurrence exists the singularity, and the concurrence reached two fixed values correspond to two different phases, i.e. Ising-like and spin liquid phase. The spin-fluid phase contains the quantum correlation while for the case of the Ising-like phase does not. In order to further analyze the critical properties of the system, we define the concurrence as the function of the dimensionless g(g= 1+γ/1-γ,γis the anisotropic parameter). We can see that the first derivative of the concurrence and gmax which is the point corresponding to maximum value of the first derivation of concurrence demonstrates their scaling behaviors and show that the transition of the system is continuous phase transition. The results obtained here are helpful to analyze the critical behavior of the XY model by means of the quantum renormalization-group approach.
Keywords/Search Tags:Quantum Entanglement, Quantum phase transition, XY model, Quantum renormalization group
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