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We have combined the idea of renormalization group and quantum informationtheory. We have shown how the entanglement or concurrence evolve as the size ofthe system being large, i.e. the finite size scaling is obtained. Moreover, Itintroduces how the renormalization group approach can be implemented to obtainthe quantum information properties of a many body system. We have obtained theconcurrence as a measure of entanglement, its derivatives and their scalingbehavior versus the size of system for the one dimensional Ising model intransverse field. We have found that the derivative of concurrence between twoblocks each containing half of the system size diverges at the critical pointwith the exponent which is directly associated with the divergence of thecorrelation length.

Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems