The Study Of Thermal Entanglement Properties In The Heisenberg Spin Chain Models With The Dzyaloshinskii-Moriya Interaction

With the development of quantum information technology, quantum entanglement has become a fundamental concept in quantum information theory. It plays an important role in the field of modern physics, quantum information processing and quantum computing. In recent years, entanglement has been regarded as a valuable resource, and people have got a lot of discussion and research on the theoretical and experimental. The entangled state can be achieved not only the behavior of classical physics is not easy to achieve, but also plays an important role in many areas such as the quantum lithography and strongly correlated quantum systems. As the simplest and most practical solid, and due to having well entanglement, the Heisenberg spin model becomes the first one of studying quantum entanglement.In this paper, we focuses on the entanglement properties of one-dimensional Heisenberg chain with spin-1/2. In the first chapter, we briefly introduce the development of quantum mechanics, quantum computation, quantum information and quantum computer. Then the definition of several concurrence are given. In the second chapter, we investigated the thermal entanglement in the two-qubit anisotropic XX model with the Dzyaloshinskii-Moriya interaction. The thermal entanglement with the variation of various parameters is calculated and analyzed. The result shows that for ferromagnetic and antiferromagnetic cases, DM interaction has different effects on the entanglement and critical temperature. Therefore, the entanglement can be controlled and enhanced by choosing appropriate DM interaction between x-component and y-component. In the third chapter, the thermal entanglement in the four-qubit anisotropic XXZ Model with the Dzyaloshinskii-Moriya interaction is firstly investigated. Then pairwise concurrence is investigated and pairwise concurrence of two nearest-neighbor qubits and two next-neighbor qubits are investigated to research this entanglement property. Then we study the thermal entanglement in the four-qubit Heisenberg XX model, where Dzyaloshinskii-Moriya interaction and external inhomogeneous magnetic field are considered. The properties of thermal entanglement of three types of pairwise concurrence are calculated. Nearest neighbor pairwise concurrence Cl2, the first category of next-nearest neighbor pairwise concurrence c13and the second category of next-nearest neighbor pairwise concurrence C24. The variation of the pairwise concurrence with various parameters is given.