We study the von Neumann entropy and related quantities in one-dimensional electron systems with on-site long-range correlated potentials. The potentials are characterized by a power-law power spectrum S(k) ∝ 1/kα, where α is the correlation exponent. We find that the first-order derivative of spectrum-averaged von Neumann entropy is maximal at a certain correlation exponent αm for a finite system, and has perfect finite-size scaling behaviors around αm . It indicates that the first-order derivative of the spectrum-averaged von Neumann entropy has singular behavior, and αm can be used as a signature for transition points. For the infinite system, the threshold value αc = 1.465 is obtained by extrapolating αm.
