Self-consistent theory of mobility edges in quasiperiodic chains

Abstract

We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localised and extended states in the space of system parameters and energy, mobility edges are generic in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-André-Harper model. The potentials in such systems are strongly and infinite-range correlated, reflecting their deterministic nature and rendering the problem distinct from that of disordered systems. Importantly, the underlying theoretical framework introduced is model-independent, thus allowing analytical extraction of mobility edge trajectories for arbitrary quasiperiodic systems. We exemplify the theory using two families of models, and show the results to be in very good agreement with the exactly known mobility edges as well numerical results obtained from exact diagonalisation.

arXiv comment5 pages, 3 figures + Supplementary Material (2 pages)

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• Exact mobility edges for 1D quasiperiodic models
• Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Quasidisorder Induced Topology
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Anderson localisation in spatially structured random graphs
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping