Entanglement and Quantum Phase Transition in Low Dimensional Spin Systems

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.