  We investigate the entanglement spectrum near criticality in finite quantum
spin chains. Using finite size scaling we show that when approaching a quantum
phase transition, the Schmidt gap, i.e., the difference between the two largest
eigenvalues of the reduced density matrix, signals the critical point and
scales with universal critical exponents related to the relevant operators of
the corresponding perturbed conformal field theory describing the critical
point. Such scaling behavior allows us to identify explicitly the Schmidt gap
as a local order parameter.
