  We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304
(R) (2007)) to study the quantum information properties of the anisotropic
s=1/2 Heisenberg chain. We have investigated the underlying quantum information
properties like the evolution of concurrence, entanglement entropy, nonanalytic
behaviours and the scaling close to the quantum critical point of the model.
Both the concurrence and the entanglement entropy develop two saturated values
after enough iterations of the renormalization of coupling constants. This
values are associated with the two different phases, i.e Neel and spin liquid
phases. The nonanalytic behaviour comes from the divergence of the first
derivative of both measures of entanglement as the size of 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.
It is shown that this exponent is directly related to the critical properties
of the model, i.e. the exponent governing the divergence of the correlation
length close to the quantum critical point. We also use a renormalization
method based on the quantum group concept in order to get more insight about
the critical properties of the model and the renormalization of entanglement.
