Exact mobility edges and coexisting extended, critical, and localized states in an extended quasiperiodic mosaic model
Phys. Rev. B 114, 134206 – Published 28 September, 2026
DOI: https://doi.org/10.1103/xy38-lztg
Abstract
Mobility edges (MEs), which separate eigenstates with distinct localization properties within a single spectrum, play a central role in localization physics. However, one-dimensional quasiperiodic models hosting analytically exact MEs, especially multiple MEs associated with critical states, remain rare. Here we propose an extended quasiperiodic mosaic model supporting two groups of exact MEs. These MEs separate extended, critical, and localized states and analytically determine both the extended-critical and critical-localized transition boundaries. We verify the exact MEs and characterize the three types of eigenstates through fractal-dimension analysis. We further introduce dynamical diagnostics based on wave-packet evolution to distinguish different localization regimes and propose an experimentally feasible realization in a Rydberg Raman superarray. Our work provides an analytically tractable platform for investigating the coexistence and dynamical signatures of different localization phases in quasiperiodic systems.
