von Neumann entropy and localization-delocalization transition of electron states in quantum small-world networks.

The von Neumann entropy for an electron in periodic, disorder, and quasiperiodic quantum small-world networks (QSWN's) is studied numerically. For the disorder QSWN's, the derivative of the spectrum-averaged von Neumann entropy is maximal at a certain density of shortcut links p*, which can be as a signature of the localization-delocalization transition of electron states. The transition point p* is agreement with that obtained by the level statistics method. For the quasiperiodic QSWN's, it is found that there are two regions of the potential parameter. The behaviors of electron states in different regions are similar to that of periodic and disorder QSWN's, respectively.