Investigation Of Quantum Correlation And Quantum Phase Transition In Heisenberg Model With Dzyaloshinskii-Moriya Interaction In An Inhomogeneous External Magnetic Field

As we know, quantum entanglement is regarded as a crucial resource due to its nonlocal nature that has been extensively used in the fields of quantum computation and quantum communication. As always, researchers have thought that quantum entanglement is the only form of quantum correlation, recently, studies have found that quantum entanglement is just one special type of quantum correlations. People discover that quantum correlation still exist even if quantum state is separate, and the disentangled state also play an important role in various quantum information processing. Therefore, It is significant to study the quantum correlation in many kinds of model, on the one hand, by using it we can explore the nature of physical phenomenon, one the other hand, it can promote the investigation of quantum information science. In this work, by considering mixed-spin(1/2, 3/2) and a two-qubit Heisenberg model, we study the three form of quantum correlations- quantum entanglement, quantum discord, and measurement-induced disturbance. In addition, we also research the behavior of quantum phase transition. Many interesting results have been discovered:1. We study the effects of the z-component of DM interaction and an inhomogeneous external magnetic field on the entanglement and quantum phase transition in mixed-spin(1/2, 3/2)Heisenberg XXZ model. Researches shows: by adjusting the parameter, we can control the ground state entanglement, and detect the quantum phase transition. At the same time, we find that the temperature and uniform magnetic field play negative effect on thermal entanglement, however, the DM interaction can enhance the critical temperature and broaden the region of entanglement.2. In order to make a comparison with entanglement, we study the measurement-induced disturbance(MID) in the above-mentioned model. We can find that we can obtain the enlargeentanglement when adjusting the anisotropy parameter, the inhomogeneity of external magnetic field and DM interaction. We note that MID, rather than N, is able to detect the quantum phase transition near J = 0 in the case of small D. It is found that DM interaction is a more efficient parameter than external magnetic field when we adjust MID under higher temperature. In addition,we also find that, for the same parameters, the critical temperature Tcof N is higher and the region of MID in our system is larger than those in mixed-spin(1/2, 1) system.3. When DM interaction and an inhomogeneous external magnetic field are included. By using the two-qubit Heisenberg XXZ model, we investigate the similarities and differences of negativity,quantum discord and measurement-induced disturbance, and the behaviors of quantum phase transition at finite temperature. Compared to the entanglement, we find that quantum discord and MID are more common measurement for quantum correlation, but it is noted that MID can not replace quantum discord in various quantum information processing. In addition, The parameters B,b, and D present the different effects on the QPT points.