Thermal Entanglement In The Heisenberg Spin Model With Magnetic Field

Quantum information science is a new product of the combination of quantum mechanics and information science from the end of 20 century, it exploits new world of the application of quantum mechanics, and provides new principle and method for the development of information science of 21 century. Quantum information science can break the physical limitation of information techniques, and solve many problems about the information management which classical information science cannot do. As the basis of the quantum information, quantum entanglement has been paid much attention both in theory study and experiment measure. As the simplest and most practical solid-state system in the quantum information field, the Heisenberg model is considered as one of the most promising physics system for the realization of quantum computation and quantum communication. The Heisenberg spin model becomes the hot of study quantum entanglement under the finite temperature, because the spin chain has well entanglement. The studies of thermal entanglement between the two qubits have gained some achievements in the Heisenberg spin model. Recently, how to obtain entanglement at the higher temperature attracts people's huge interest.In this thesis, we cite the concept-negativity, and study the thermal entanglement of (1/2,1) mixed-spin Heisenberg model under the non-uniform magnetic field. Firstly, we study an isotropic Heisenberg XY model, and analyze the effects of the spinning interaction parameterλand the inhomogeneous magnetic field b on entanglement. We find that the biggest entanglement and the critical temperature of entanglement increase along with the spinning interaction parameterλ, it means that the spinning interaction parameter can control the effects of temperature on entanglement, we can obtain entanglement under the higher temperature through adjust the spinning interaction parameterλ. In addition, the critical temperature of entanglement increase along with the inhomogeneous magnetic field b; but the biggest entanglement under the non-uniform magnetic is smaller than it under the uniform magnetic, so the inhomogeneous magnetic field b cannot enhance the biggest entanglement. This means that the inhomogeneous magnetic field b can also control the effects of temperature on entanglement, thus we can enhance the critical temperature of entanglement through adjust the inhomogeneous magnetic field b, and then we can find the best entanglement under the limited temperature although it will reduce the biggest entanglement.Finally, we study the anisotropic Heisenberg XY model, and discuss the effects of the anisotropic parameter y and the inhomogeneous magnetic field b on entanglement. We find that the biggest entanglement and the critical temperature of entanglement increase along with the anisotropic parameter y, it means that the anisotropic parameter y can also control the effects of temperature on entanglement, We can obtain entanglement under the higher temperature through adjust the anisotropic parameterγ. The inhomogeneous magnetic field b can enhance the critical temperature of entanglement, but it cannot enhance the biggest entanglement, it is a same finding as isotropic model. In addition, we study the entanglement under the absolutely non-uniform magnetic, and analyze the change of negativity along with the temperature T and the inhomogeneous magnetic field b. We find that the entanglement quickly increase to the maximum first, and then reduce slowly; we also find that the system that under the absolutely non-uniform magnetic has a big critical temperature.