Mixed Ising Spin System Of One-dimensional Quantum Entanglement

Since the notion of quantum entanglement was advanced by Schrodinger, quantum entanglement attracted wide attention. Especially, with the development of the quantum information science, which is crossed marginal subject, people deeply study quantum entanglement. Due to its character, quantum entanglement obtain wide application in the quantum information, especially in quantum teleportation and quantum coding.The development of the quantum information theory arose many other field attention and interest, especially condensed matter. The search of quantum system, which adapts to physical realization of quantum computation, and the study the more controlling conditions contrast to traditional solid system become the important field in condense physics. On the physical realization of quantum entanglement under the finite temperature, Heisenberg spin system becomes the hot study. How to obtain entanglement at the higher temperature attracts people's huge interest. In the modern condense physics, quantum phase transition is a study hotspot. Entanglement is the quantum correlation, which does not exist in classical system. So using the issue of the quantum entanglement to know quantum phase transition can help us to achieve new understand.In this thesis, we study the properties of thermal entanglement of some mixed-spin Heisenberg system. Firstly, we study the phenomenon about thermal entanglement of a two mixed-spin Heisenberg XY chain with a uniform magnetic field. We find that magnetic field and anisotropic parameter can suppress the effects of temperature on entanglement, and that we are able to obtain entanglement at higher temperature by adjusting magnetic field and anisotropic parameter. Besides, quantum phase transition occurs at zero temperature, and the phase transition point is shifted to low magnetic field if temperature keeps low as the anisotropic parameter is increased. For Ising model, thermal entanglement still exists without magnetic field. Finally, we give the study on entanglement of two mixed-spin Heisenberg XXZ chain with an inhomogeneous magnetic field. We can obtain entanglement at higher temperature with an inhomogeneous magnetic field contrast to uniform magnetic field. Moreover, we find that quantum occurs twice at zero temperature and that entanglement appears step-form change. These results indicate that anisotropic parameter and the degree of inhomogeneous magnetic field can be used to open and close entanglement.