Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials

Abstract

We obtain approximate solutions defining the mobility edge separating localized and extended states for several classes of generic one-dimensional quasiperiodic models. We validate our analytical ansatz with exact numerical calculations. Rather amazingly, we provide a single simple ansatz for the generic mobility edge, which is satisfied by quasiperiodic models involving many different types of nonsinusoidal incommensurate potentials as well as many different types of long-range hopping models. Our ansatz agrees precisely with the well-known limiting cases of the sinusoidal Aubry-André model (which has no mobility edge) and the generalized Aubry-André models (which have analytical mobility edges). Our work provides a practical tool for estimating the location of mobility edges in quasiperiodic systems.

arXiv comment8 pages, 7 figures

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• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Flux enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a Bose-Hubbard ladder
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Quantum localization in incommensurate tight-binding chains
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Many-body localization in a slowly varying potential