Exact Mobility Edges in One-Dimensional Mosaic Lattices Inlaid with Slowly Varying Potentials

Abstract

We propose a family of one-dimensional mosaic models inlaid with a slowly varying potential $V_n=\lambda\cos(\pi\alpha n^\nu)$, where $n$ is the lattice site index and $0<\nu<1$. Combinating the asymptotic heuristic argument with the theory of trace map of transfer matrix, mobility edges (MEs) and pseudo-mobility edges (PMEs) in their energy spectra are solved semi-analytically, where ME separates extended states from weakly localized ones and PME separates weakly localized states from strongly localized ones. The nature of eigenstates in extended, critical, weakly localized and strongly localized is diagnosed by the local density of states, the Lyapunov exponent, and the localization tensor. Numerical calculation results are in excellent quantitative agreement with theoretical predictions.