Exact multiple anomalous mobility edges in a flat band geometry

Anomalous mobility edges (AMEs), separating localized from multifractal critical states, represent a novel form of localization transition in quasiperiodic systems. However, quasi-periodic models exhibiting exact AMEs remain relatively rare, limiting the understanding of these transitions. In this work, we leverage the geometric structure of flat band models to construct exact AMEs. Specifically, we introduce an anti-symmetric diagonal quasi-periodic mosaic modulation, which consists of both quasi-periodic and constant potentials, into a cross-stitch flat band lattice. When the constant potential is zero, the system resides entirely in a localized phase, with its dispersion relation precisely determined. For non-zero constant potentials, we use a simple method to derive analytical solutions for a class of AMEs, providing exact results for both the AMEs and the system’s localization and critical properties. Additionally, we propose a classical electrical circuit design to experimentally realize the system. This study offers valuable insights into the existence and characteristics of AMEs in quasi-periodic systems.