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 vertical bar i-j vertical bar 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.