  We have composed the ideas of quantum renormalization group and quantum
information by exploring the low energy states dynamic of entanglement
resources of a system close to its quantum critical point. We demonstrate the
low energy states dynamical quantities of the one dimensional magnetic systems
could show the quantum phase transition point and shows the scaling behavior in
the vicinity of the transition point. To present our idea, we study the
evolution of two spins entanglement in the one-dimensional Ising model in the
transverse field. The system is initialized as the so-called thermal ground
state of the pure Ising model. We investigate evolvement of the generation of
entanglement with increasing the magnetic field. We have obtained that the
derivative of the time at which the entanglement reaches its maximums with
respect to the transverse field, diverges at the critical point and its scaling
behaviors versus the size of the system are as same as the static ground state
entanglement of the the system.
