Two-Point Entanglement Near a Quantum Phase Transition

In this work, we study the two-point entanglement S(i,j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system, near a quantum phase transition. Away from the critical point, S(i,j) saturates with a characteristic length scale $\xi_E$, as the distance |i-j| increases. The entanglement length $\xi_E$ agrees with the correlation length. The universality and finite size scaling of entanglement are demonstrated in a class of exactly solvable one dimensional spin model. By connecting the two-point entanglement to correlation functions in the long range limit, we argue that the prediction power of a two-point entanglement is universal as long as the two involved points are separated far enough.