New approach to localization: Quantum connectivity

Abstract

We introduce the concept of quantum connectivity, which, along with the phenomenological renormalization method, allows us to study the localization of one-electron eigenstates of various disordered tight-binding Hamiltonians. For the site quantum percolation model in three dimensions we find that the quantum percolation threshold is ${p}_{q}$=0.48\ifmmode\pm\else\textpm\fi{}0.01. For the Anderson model we find that the critical disorder is ${W}_{c}$/J=15.95\ifmmode\pm\else\textpm\fi{}0.25. For a topologically disordered model with exponential interactions of range a, we find that the dimensionless critical density parameter ${\mathit{R}}_{\mathit{c}}$=${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}^{1/3}$a=0.257\ifmmode\pm\else\textpm\fi{}0.014.