# Localization-delocalization transitions in a two-dimensional quantum percolation model: von Neumann entropy studies

## TL;DR

This study investigates the localization-delocalization transition in a 2D quantum percolation model using von Neumann entropy, revealing a quantum percolation threshold below 1 and non-universal critical exponents.

## Contribution

It provides the first numerical evidence of a quantum percolation threshold less than 1 in 2D, using von Neumann entropy to analyze phase transitions.

## Key findings

- Maximal derivative of von Neumann entropy at $p_q$ indicates transition point
- Quantum percolation threshold $p_q$ is approximately 0.665
- Critical exponents are non-universal

## Abstract

In two-dimensional quantum site-percolation square lattice models, the von Neumann entropy is extensively studied numerically. At a certain eigenenergy, the localization-delocalization transition is reflected by the derivative of von Neumann entropy which is maximal at the quantum percolation threshold $p_q$. The phase diagram of localization-delocalization transitions is deduced in the extrapolation to infinite system sizes. The non-monotonic eigenenergies dependence of $p_q$ and the lowest value $p_q\simeq0.665$ are found. At localized-delocalized transition points, the finite scaling analysis for the von Neumann entropy is performed and it is found the critical exponents $\nu$ not to be universal. These studies provide a new evidence that the existence of a quantum percolation threshold $p_q<1$ in the two-dimensional quantum percolation problem.