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

TL;DR

This paper investigates how von Neumann entropy can signal localization-delocalization transitions of electron states in quantum small-world networks, revealing a correlation with spectral statistics and potential parameter regions.

Contribution

It introduces the use of von Neumann entropy to identify phase transitions in quantum small-world networks, aligning with level statistics results and exploring effects of quasiperiodic potentials.

Findings

Maximal derivative of von Neumann entropy indicates transition point p* in disordered networks.

Transition point p* agrees with level statistics method.

Electron states exhibit behaviors similar to periodic and disordered networks in different potential regions.

Abstract

The von Neumann entropy for an electron in periodic, disorder and quasiperiodic quantum small-world networks(QSWNs) are studied numerically. For the disorder QSWNs, 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 QSWNs, 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 QSWNs, respectively.