Quantifying the levitation picture of extended states in lattice models

The behavior of extended states is quantitatively analyzed for two-dimensional lattice models. A levitation picture is established for both white-noise and correlated disorder potentials. In a continuum limit window of the lattice models we find simple quantitative expressions for the extended states levitation, suggesting an underlying universal behavior. On the other hand, these results point out that the quantum Hall phase diagrams may be disorder dependent.