| Based on the entanglement at zero temperature, we study the thermal entanglement in anisotropic XY model in a transverse field at finite temperature . The behaviors of the thermal entanglement of three cases of the XY chains: uniform chain, period-two and period-three chains, are studied by using the concurrence. It is found that for some anisotropic parameters, there is a region of the exchange interaction, in which the thermal entanglement has more than one critical temperatures. At the same time we give the region of anisotropic parameter in which this phenomenon happened. We also discuss the behavior of the thermal entanglement at the vicinity of quantum phasetransition of periodic anisotropic XY chains and find that all the derivatives (?)_λC havethe similar behaviors as that of uniform chain.Then we study the partial entropy of entanglement of this model at a finite temperature. As a simple example, we study the partial entropy of entanglement of three qubits system. It is found that the partial entropy of one subsystem isn't equivalent to that of the other subsystem, which isn't the same with the partial entropy at zero temperature. Then we study the partial entropy of entanglement of infinite spin chain, which also have the similar behavior as the three spin chain, so we introduce the concept of mutual entropy. We study the mutual entropy of this model and find that the mutual entropy is symmetrical with increasing the number of spins of subchain. And mutual entropy decays exponential with increasing temperature. We also give the plots of mutual entropy as function of temperature, number of spins of subchain and the nearest neighbor interaction.Finally, by using the concept of negativity, we investigate the thermal entanglement of (1/2,1) mixed-spin anisotropic XY model and obtain the numerical results of the thermal entanglement of two spins in a transverse field at finite temperature. We find that there exists a critical temperature, after which the entanglement vanishes. |
PDF Full Text Request