Renormalization of concurrence: Quantum information properties close to quantum critical point via the renormalization group

My presentation is a collection of our recent investigations on the quantum information properties of spin models close to the quantum critical points. I first introduce the implementation of quantum renormalization group to get the quantum critical properties of a spin model. This implementation is used to show the evolution and finite size scaling of entanglement and its derivative close to quantum critical point of the Ising model in transverse magnetic field (ITF). The finite size analysis of the entanglement derivative is presented. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length. From the same point of view the quantum phase transition of XXZ model from the Neel phase to the spin liquid one is presented. The non-analytic behavior comes from the divergence of the first derivative of both measures of entanglement as the size of the system becomes large. The renormalization scheme demonstrates how the minimum value of the first derivative and its position scales with an exponent of the system size. We have also investigated the effect of Dzyaloshinskii-Moriya interaction on the quantum information properties of ITF and XXZ model close to their quantum critical boundaries. Finally, the most recent results are presented on the connection between quantum information property and quantum critical point of the Kondo-necklace model which is obtained by the continuous unitary transformations.