Quantum Entanglement And Quantum Phase Transition In The XY Model With Staggered Dzyaloshinskii-Moriya Interaction

Quantum entanglement is one of the most string features of quantum theory and is also regarded as a fundamental resource. It has been widely used in quantum computation, quantum cryptographic key distribution, quantum teleportation and so on. In recent years, the researchers have found that the quantum entanglement plays an important role in the quantum phase transition. The quantum critical property of the spin system can be described by the concept of entanglement. We study the quantum entanglement and quantum phase transition of the anisotropic S=1/2 model with staggered Dzyaloshinskii-Moriya (DM) interaction by using the quantum renormalization group (QRG) method.With the help of the Kadanoff's block method, two stable fixed points and an unstable fixed point are obtained, which correspond with spin-fluid phase, Neel phase and the phase transition point, respectively. The concurrence is considered as a measure of the quantum correlation. The analytical expression of the concurrence can be gotten by the reduced density matrix of the system which is the function of anisotropy parameter and DM interaction. The variation tendency of the concurrence at the critical point, the nonanalytic behavior of the first derivative concurrence and the scaling behavior of the system can be also obtained. We study the concurrence how changes versus the anisotropy parameter and DM interaction, respectively. It is found that both of them can influence the phase diagrams. As the number of RG iterations increases, the concurrence develops two different values for a given value of DM interaction which correspond with the spin-fluid and Neel phases, respectively. For Nccl phase, the larger the value of DM interaction is, the wider the width of value of anisotropy parameter is. Further insight, the first partial derivative of the concurrence exhibits the nonanalytic behavior at the thermodynamic limit, it is shown that the system occurs quantum phase transition. For a given value of anisotropy parameter, we can also obtain the similar results. The scaling behavior can be obtained which characterizes how the critical point of the model is touched as the size of the system increases. At last, we get the relation between the critical exponent and correlation length exponent, and find that there exist the relationship of reciprocal.