  We investigate the quantum phase transitions for the $XXZ$ spin-1/2 chains
via the quantum correlations between the nearest and next to nearest neighbor
spins characterized by negativity, information deficit, trace distance discord
and local quantum uncertainty. It is shown that all these correlations exhibit
the quantum phase transitions at $\Delta=-1$. However, only information deficit
and local quantum uncertainty can demonstrate quantum phase transitions at
$\Delta=1$. The analytical and numerical behaviors of the quantum correlations
for the $XXZ$ system are presented. We also consider quantum correlations in
the Hartree-Fock ground state of the Lipkin-Meshkov-Glick (LMG) model.
