  Entanglement of the ground states in $XXZ$ and dimerized Heisenberg spin
chains as well as in a two-leg spin ladder is analyzed by using the spin-spin
concurrence and the entanglement entropy between a selected sublattice of spins
and the rest of the system. In particular, we reveal that quantum phase
transition points/boundaries may be identified based on the analysis on the
local extreme of this entanglement entropy, which is illustrated to be superior
over the concurrence scenario and may enable us to explore quantum phase
transitions in many other systems including higher dimensional ones.
