| Quantum entanglement and quantum correlation are important properties of quan-tum theory,and they are important resources for the application of quantum information science.Therefore,they have attracted the attention of a large number of researchers at home and abroad.The realization of quantum information tasks and quantum comput-ing schemes need to rely on physical reality.Therefore,multi-body systems with actual material background have been widely concerned.Nowadays,the study of quantum entan-glement and quantum correlation in multi-body system mainly focuses on three aspects:Firstly,using the tools and methods of quantum information theory to study the proper-ties of multi-body systems,and using quantum entanglement and quantum correlation to study quantum phase transitions is one of the research hotspots.Secondly,the quantum entanglement and quantum correlation of multi-body system are studied with the change of system parameters.Thirdly,the application of quantum entanglement and quantum correlation in multi-body system is studied.Recently,the infinite Ising-Heisenberg diamond chains reflecting the structure and properties of azurite(Cu3(CO3)2(OH))crystal materials and the infinite Ising-Heisenberg branching chains reflecting the heterotrimetallic chains[Cu Mn(L)][Fe(bpb)(CN)2].Cl O4.H2O(Fe-Mn-Cu for short)have attracted the interest of researchers.The research on Ising-Heisenberg diamond chains focuses on its ground state properties and thermal entan-glement at finite temperature,while the research on Ising-Heisenberg branched chains focuses on its phase transition,magnetic properties and entanglement properties.There-fore,this article mainly through transfer matrix method research has Dzyaloshinskii-Moriya(DM)the interaction of infinitely long Ising-Heisenberg diamond chain and Ising-Heisenberg branched chain of quantum entanglement and quantum correlation describe quantum phase transition,as well as the finite temperature,two Ising-Heisenberg chain of quantum entanglement and quantum correlation with the change of parameters,and finally discuss Ising-Heisenberg diamond chain and Ising-Heisenberg branched chain of Heisenberg dimer as quantum channel to realize quantum dense coding and quantum teleportation.The structure and main achievements of this thesis are as follows:In chapter 1,we introduce the background of our thesis.In chapter 2,we introduce the research background of quantum entanglement,quan-tum detuning,quantum phase transition,quantum teleportation,quantum dense coding and so on.In chapter 3,we study the ground state of an infinite Ising-Heisenberg diamond chain with DM interaction;The thermal quantum discord and the entanglement of formation are used to characterize the quantum phase transition;And the variation of thermal quantum correlation with parameters in the system;Finally,the Heisenberg dimer as a quantum channel for quantum dense coding is discussed.Here's what the study found:Firstly,we study the ground state of Ising-Heisenberg diamond chains with DM interactions.It is found that considering the DM interaction along the z direction,the anisotropic phase transition points are changed,while the external magnetic field and Ising-Heisenberg coupling phase transition points are not changed.In addition,when the intensity of the external magnetic field is different from the anisotropy,the DM interaction can induce different phase transitions.Secondly,thermal quantum discord(TQD)and the entanglement of formation(E-OF)are used to characterize the phase transition points of Ising-Heisenberg diamond chain with DM interaction at finite temperature.It is found that the TQD and EOF of Ising-Heisenberg diamond chain and their corresponding first-order conduction energies represent the quantum phase transition points of the ground state of the system at a given temperature.Thirdly,thermal quantum discord and thermal quantum entanglement are used to study the thermal quantum correlation in Ising-Heisenberg diamond chains with DM interaction.It is found that the thermal quantum discord and quantum entanglement in the system are not only affected by the external temperature,but also related to the strength of DM interaction,anisotropy and Heisenberg coupling in the system.Fourthly,the standard quantum dense coding scheme is used to investigate the quan-tum channel realization of the Heisenberg dimer in the Ising-Heisenberg diamond chain with DM interaction.It is found that the quantum dense coding capacity and the first-order derivatives of the system can represent the quantum phase transition when the temperature is low.In addition,the density coding capacity can be increased by increas-ing the anisotropy and DM interaction of the system,while the density coding capacity can be increased by increasing the external temperature.In chapter 4,a standard quantum teleportation protocol is used to transfer any two qubit entangled states,and a Heisenberg dimer in a spin-1/2 infinitely long Ising-Heisenberg branch chain is used as a quantum channel to study the quantum teleportation of this channel.It is found that increasing the entanglement degree of the input state and the anisotropy can increase the entanglement degree of the output state,thus affecting the performance of quantum teleportation–the average fidelity FA.In chapter 5,we use Negativity to study the quantum entanglement in the infinitely long Ising-Heisenberg branched chain with mixed spin-(1/2,5/2,1/2).It is found that the Negativity and the first derivative can characterize the quantum phase transition of the ground state of the system when the temperature is close to zero.The negative en-tanglement of the system is related to the external temperature,magnetic field strength,Ising-Heisenberg coupling strength and anisotropy.When the system is in an isotropic system,the maximum entanglement degree decreases gradually with the increase of Ising-Heisenberg coupling strength,but the critical temperature increases.At higher tem-perature,a certain magnetic field intensity can promote the generation of entanglement.When the magnetic field intensity is high,the phenomenon of entanglement”recovery”will appear.As the anisotropy increases.The change of negative entanglement reflects non-monotonicity.At the end of thesis,we will make a summary and prospect of our studies. |
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