  Combining the ideas of quantum Fisher information and quantum renormalization
group method, the Berezinskii-Kosterlitz-Thouless quantum phase transition of
spin- 1/2 XXZ chain is investigated. Quantum Fisher informations of the whole N
sites and the partial N/3 sites are studied. They display very similar
behaviors, even though their mathematical formulas are very different from each
other. The universally critical exponent of quantum Fisher information is
obtained as beta=0.47, which is consistent with the results obtained by the
renormalized concurrence or discord. We also discuss the relationship between
quantum Fisher information and entanglement
