The Study Of Thermal Entanglement In Quantum Heisenberg Model

In the 20th century, quantum mechanics expand a new area that is quantum information, and quantum entanglement is the key. Quantum entanglement is a wonderful phenomenon which presented in many subsystems of quantum systems, and because of non-local features entanglement has been used as a potentially valuable resource in quantum computing, quantum information processing and plays an important role. By the concept of Negativity, in this paper we research the property of entanglement in Heisenberg XY model and XXZ model and we get some interesting conclusions. Specific study in this article as follows:For Heisenberg XY model with DM interaction D and magnetic field B we study the influence of different parameters to entanglement. Through calculation we known that B can change the value and the feature of entanglement at low temperature, and it affects the critical temperature based on the value of anisotropy. It is easily to find that D does not change the revival feature, and it only affects the area near critical magnetic field Bc and adjusts the value of Bc. As J increased the maximum of entanglement are all the same, no matter what the value of B and D are.Then we study the thermal entanglement in Heisenberg XXZ model with DM interaction. Through calculation, we know that for XXZ model the anisotropy and spin can be used together to control the extent of entanglement and, in particular, to obtain large entanglement The effect of spin in both models show that it can increase the critical temperature and the negativity decreases as the spin increases. We found that the DM interaction has different effects on fermi and bose systems so it can not only excite entanglement but also affect the entanglement in different spin systems.We investigate the ground-state and thermal entanglement in spin-1 Heisenberg XXX model and XXZ model with DM interaction, and in order to get better conclusion we study this system compared to the system of (1/2,1/2) and (1/2,1). We find that the entanglement is maximum in (1/2,1/2) and is minimum in (1/2,1) which means the fermi system has significant effect to the entanglement. We get that the critical temperature in (1,1) is biggest than that in (1/2,1/2) and (1/2,1) which has practical significance to obtain entanglement at high temperature, and in (1,1) the critical temperature of J>0 is almost the same to that of J<0 which is different form the other cases.