Hidden self-duality and exact mobility edges in quasiperiodic network models

Abstract

In one-dimensional quasiperiodic systems, only a few models with exact mobility edges (MEs) have been constructed using generalized self-duality theory, Avila's global theory, or the renormalization group method. This raises an intriguing question that whether we can realize more physical models with exact solvable MEs. In this work, we uncover the hidden self-duality within a class of quasiperiodic network models constituted by periodic and quasiperiodic sites. Although the original Hamiltonians appear to lack self-duality, their effective Hamiltonians obtained by integrating out the periodic sites exhibit self-duality, which yield MEs. The well-studied mosaic model, which is the simplest case of quasiperiodic network models, was previously thought to exhibit MEs due to the absence of self-duality, but we show that they actually arise from the hidden self-duality. Using the effective Hamiltonian, we further introduce the concept of resonant states to understand the shape of MEs. Finally, we present in detail how to determine the MEs in various network models, including some non-Hermitian models, based on the hidden self-duality. These predictions can be experimentally realized using optical and acoustic waveguide arrays. Our work can greatly advance our understanding of MEs in Anderson transition.