Exact Mobility Edges in 1D Mosaic Lattices Inlaid with Slowly Varying Potentials. Issue 11 (3rd October 2021) - Gong, Long‐Yan; Lu, Hui; Cheng, Wei‐Wen
Abstract: A family of 1D mosaic models inlaid with a slowly varying potential is proposed. Combining the asymptotic heuristic argument with the theory of trace map of transfer matrix, mobility edges (MEs), and pseudo‐MEs (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, pseudo‐critical, and strongly localized is diagnosed by the local density of states, the Lyapunov exponent, the localization tensor, and fractal dimension. Numerical calculation results are in excellent quantitative agreement with theoretical predictions. Abstract : A family of 1D mosaic models inlaid with a slowly varying potential is proposed. The phase diagram is obtained semi‐analytically, which includes extended, critical, weakly localized, pseudo‐critical, and strongly localized phases. There exist mobility edges and pseudo‐mobility edges. Numerical results, that is, the local density of states, the Lyapunov exponent, the localization tensor, and the fractal dimension, verify theoretical predictions.