Dynamics Of Quantum Entanglement Of One Dimensional Anisotropic XY System

Quantum entanglement is an important method in Quantum Information and Quantum Computing technology. By calculating the quantum entanglement, some of the classic physics problem that could not be solved, such as quantum transfer, quantum dense coding and quantum cryptography could find their solutions. Quantum entanglement and dynamics of quantum entanglement have become a hot research topic in recent years. In this work the method of quantum renormalization group was used to discuss the issue of the dynamics of quantum entanglement with the one-dimensional anisotropic XY model which has staggered Dzyaloshinskii-Moriya(DM) interaction.We could use the quantum renormalization group method to acquire the renormalization group equation of the system, and acquire the time-dependent density matrix by the time evolution. Because the quantum correlation of the system could be described by the system’s concurrence which is a function of anisotropy, DM interaction and time t, we could obtain the analytical expression of the system’s concurrence by its time-dependent density matrix. We analyzed the relation of system’s concurrence, anisotropy parameter, DM interaction and time found that when the DM interaction happens, time constants value, with the increase of the number of iterations of renormalization and the change of anisotropy parameters, the changing frequency decreases and with the emerge of the anisotropy parameters, its trend is same to the trends at time zero. And when the time becomes large, entanglement change in frequency will also be larger. The time when the entanglement reaches the maximum for the first time with changing anisotropy parameters shows that time approaches zero as the parameters change and becomes larger as system scale increases. As a result of analysis, the logarithm of absolute derivative of the time when the entanglement reaches the maximum for the first time and anisotropy has a scaling behaviors with the logarithm of system scale. At last,we studied the monogamy of quantum correlations of concurrence and found that concurrence obeys the monogamy properties as time goes on.