The Properties Of Entanglement And Phase Transition In Quantum Spin Models

Quantum spin systems which exist rich entanglement properties, have attracted widespread attention in recent years, and play an important role in quantum information,quantum key distribution, and other fields. In this thesis, we use the virtual-site correlation mean field theory to study the entanglement of the spin-1/2 Ising, XY, and XXZ models with Dzyaloshinskii-Moriya interaction. In addition, We study the phase transitions of Ising model in detail.In the second chapter of the thesis, we apply virtual-site correlation mean field theory to research the entanglement and phase transition of the spin-1/2 Ising, XY, and XXZ models with Dzyaloshinskii-Moriya interaction in the thermodynamic limit N??.Through the analysis of the correlator, we can predict the phase transitions in the system.In addition, we take the negativity as a measure to investigate the entanglement of this system and study the influence of temperature T, DM interaction on the entanglement.For Ising model, we can see when the DM interaction at a certain value, the entanglement is decreased with the increase of temperature and when at a certain temperature, along with the rising of the DM interaction, the entanglement is increased; For XY, XXZ models, it was found that when the temperature is very low, with the increase of DM interaction or decrease of anisotropic parameter, the maximum of the entanglement don’t change,but the critical temperature is gradually increased.In the third chapter of thesis, we apply virtual-site correlation mean field theory to research the entanglement and phase transition of the spin-1/2 transverse Ising, XY, and XXZ models with Dzyaloshinskii-Moriya interaction in the thermodynamic limit N??.It was found that when the temperature is very low, with the DM interaction increases or anisotropic parameter decreases, the maximum of the entanglement don’t change,but the critical temperature is gradually increased. When DM interaction, and the anisotropic parameter is a constant value, entanglement will appear the phenomenon of "renewable" while it changes with temperature and external field; When DM interaction and additional magnetic field is a constant value, anisotropic parameter and critical temperature exist certain linear relationship. Compared the situation with no external magnetic field, there have a big difference, such as entanglement threshold temperature sometimes become larger, etc., which are of great help to the use of entanglement.At the end of the thesis, we give the summary and outlook.