Thermal Entanglement Of Heisenberg Model In A Magnetic Field

As the basis of the quantum information, quantum entanglement has been paid much atention both theoretically and experimentally. The thermal entanglement in the Heisenberg model may really have applications in many fields. Many studies have focused on the thermal entanglement between the nearest-neighbor qubit in the Heisenberg model.In this thesis, the introduction about entanglement, quantum teleportation and the Heisenberg model is given firstly. Then, the two-qubit Heisenberg XYZ model under an inhomogeneous z-axis magnetic field is studied. The influence of the direction of magnetic field on entanglement in Heisenberg XXZ model is studied. Both the uniform and nonuniform fields are addressed. The thermal entanglement in a Sin-1 system with two spin coupled by exchange interaction is investigated, both the effects of inhomogeneous magnetic field and couplings being considered.It is found that the influence of magnetic field on the entanglement is in evidence and depends on the couplings. The average and difference values of the magnetic field on two qubits behave symmetry, as the z-component coupling crossing a critical value which depends on the other two couplings. Changing the direction of the filed could control the entanglement of antiferromagnetic model, influence behavior of the entanglement of ferromagnetic model. The difference of the direction of magenetic field on two qubits can induce and inhance the entanglement of Heisenberg model. A suitable inhomogeneous magnetic field may conduce the entanlment of Spin-1 XX model. The entanglement of Spin-1 XXZ model is enhanced by increasing the interaction of z-component . With the increase of the anisotropy in the XY plane, the maximum value of entanglement declines, but the entanglement in a lager magnetic field is improved. Jz...