The Study Of Negativity Of Heisenberg Spin Systems

Quantum entanglement is studied intensively as an important resource of quantum communication and quantum computation.Moreover,Heisenberg spin system,which is abundant in quantum properties,is regarded as a natural candidate in the solid state proposals of realizing quantum computing.Considering real circumstance,the study of thermal entanglement becomes the point of the research of entanglement.Up to now,people not only study thermal entanglement properties in the Heisenberg spin system theoretically,but also a lot of work on the entanglement properties of magnetic materials have done by experiment.In this thesis,we choose the spin model which have real material background as the research object,for example,Na₉[Cu₃Na₃?H₂O?₉(-AsW₉O₃₃)₂]·26H₂O?denoted as{Cu₃}for convenience?and Ising-Heisenberg diamond chain,and numerical method is used to study the thermal entanglement properties.1.We adopt tripartite negativity to study the thermal entanglement of{Cu₃}single molecule magnet with magnetic field in thermal equilibrium.We consider the magnetic fields along the vertical and the parallel directions of triangular spin ring,respectively,and the case with a tilted magnetic field is also discussed in this thesis.The result shows that the magnetic intensity,the direction of magnetic field and temperature has important influence on the tripartite negativity of system.Moreover,we also obtain the range of parameters in which the tripartite entanglement of the system exists.Therefore,the properties of the tripartite entanglement in the{Cu₃}triangular spin ring can be controlled and enhanced by choosing appropriate magnitude and direction of the magnetic field and temperature.2.We use the transfer matrix method to study the thermal entanglement of spin-1Ising-Heisenberg diamond chain with biquadratic interaction.According to the anisotropy,we study the negativity of the Ising-XXX coupling model and Ising-XXZ coupling model with the change of magnetic field and temperature.It is shown that,in isotropic Heisenberg?Ising-XXX?coupling model,the thermal entanglement can be induced by the biquadratic interaction in the case with ferromagnetic coupling and antiferromagnetic coupling when the magnetic field is absented,especially the case with ferromagnetic coupling.The external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction in the case with ferromagnetic coupling.Moreover,the biquadratic interaction makes the threshold temperature and magetic field increase in anisotropic Heisenberg?Ising-XXZ?coupling model.The critical temperature and magnetic fields become larger when the anisotropy strength is tronger.So our result can be a reference for the magnetic compounds which can be used in the area of quantum information and quantum computation.3.We study the thermal entanglement of Ising-Heisenberg chain with triangular plaquettes.The tripartite negativity and concurrence are calculated by means of transfer matrix method.It shows that the result of concurrence is better than the negativity.Along with magnetic field intensity and temperature will effect on the entanglement of three kinds of Heisenberg?XXX,XXZ,XYZ?coupling model.Besides the variations of the critical temperature with the magnetic field in three cases,it shows that the range of parameters in which the tripartite entanglement of the system exists in three case.Our study provide guidance significance as controlling the thremal entanglement of Ising-Heisenberg chain with triangular plaquettes.