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

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 $p_q\simeq 0.665$ 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.

7 pages, 5 figures

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• Quantum percolation on Lieb Lattices
• Spectral approach to transport in the 2D honeycomb lattice with substitutional disorder
• How the site degree influences quantum probability on inhomogeneous substrates
• Killing the Hofstadter butterfly, one bond at a time
• Coexistence of extended and localized states in one-dimensional systems
• Effects of critical correlations on quantum percolation in two dimensions
• Entanglement signatures of a percolating quantum system