The Heisenberg Xx And Xxx Models Of Quantum Entanglement And Quantum Phase Transition,

As an essential quantum information resource, quantum entanglement can realize many quantum information protocols which are difficult to be realized by classical methods and have the characteristics of natural security, ultra-high speed, large-capacity, such as quantum cryptography, quantum teleportation et al. The investigation concerning quantum entanglement is wide from its basic definitions and measurement to the generation and manipulation of entangled states and so on. Whether for the basic theory of quantum information or potential future practical applications, quantum entanglement's in-depth study will have far-reaching impact on them. Due to the easy integration and scalability, solid state are the promising candidates for realizing quantum computation in quantum information processing especially in the physical realization of quantum computing. A large number of literatures show that spin chain is one of the systems used for quantum communication and quantum computation. It is helpful to explain and discover new physical phenomena to study the entanglement of many-body systems, such as spin chain.Quantum entanglement and quantum phase transitions are all important areas of theoretical physics, and there are many methods of calculation of quantum entanglement, such as the partial entropy of entanglement and entanglement of formation and concurrence and negativity and so on. In this paper, we mainly investigate that quantum phase transition and entanglement in Heisenberg XX spin chain with impurity and thermal entanglement in HeisenbergⅩⅩⅩmodel of two spin-1/2 particles under external magnetic fields.The main results of this thesis are as follows:1. we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears and has a corresponding relation to the quantum entanglement when impurity parameter is an arbitrary constant. The external magnetic field and impurity parameters have a great effect on quantum phase transition and quantum entanglement. By modulating the temperature, magnetic field and.the impurity parameters, the entanglement between any two lattices can exhibit a platform-like behavior, which can be used to realize entanglement switch.2. To investigate the thermal entanglement and its regulation in the presence of uniform magnetic field and inhomogeneous field in Heisenberg XXX model, we exert two controllable magnetic fields on coupled two-qubit system, and calculate the concurrence of the system, and then we have a comparison of concurrence in these two conditions. Moreover, We have a discuss about the relationship between the critical temperature and external magnetic field, and find that by controlling the inhomogeneous magnetic field b we can enhance the critical temperature of dead entanglement greatly.