Mobility Edges in one-dimensional Models with quasi-periodic disorder

Abstract

We study the mobility edges in a variety of one-dimensional tight binding models with slowly varying quasi-periodic disorders. It is found that the quasi-periodic disordered models can be approximated by an ensemble of periodic models. The mobility edges can be determined by the overlaps of the energy bands of these periodic models. We demonstrate that this method provides an efficient way to find out the precise location of mobility edge in qusi-periodic disordered models. Based on this approximate method, we also propose an index to indicate the degree of localization of each eigenstate.

arXiv comment15 pages, 3 figures

References in corpus (21)

• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Topological phases of generalized Su-Schrieffer-Heeger models
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• One-dimensional quasicrystals with power-law hopping
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
• Anderson localization transitions with and without random potentials
• Anomalous transport through algebraically localized states in one-dimension
• Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices
• Novel mobility edges in the off-diagonal disordered tight-binding models
• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Enhancing coherence of a state by stochastic strictly incoherent operations
• Persistence of chirality in the Su-Schrieffer-Heeger model in the presence of on-site disorder
• Fate of topological states in incommensurate generalized Aubry-André models

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• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential