Nearest neighbor tight binding models with an exact mobility edge in one dimension

Abstract

We investigate localization properties in a family of deterministic (i.e. no disorder) nearest neighbor tight binding models with quasiperiodic onsite modulation. We prove that this family is self-dual under a generalized duality transformation. The self-dual condition for this general model turns out to be a simple closed form function of the model parameters and energy. We introduce the typical density of states as an order parameter for localization in quasiperiodic systems. By direct calculations of the inverse participation ratio and the typical density of states we numerically verify that this self-dual line indeed defines a mobility edge in energy separating localized and extended states. Our model is a first example of a nearest neighbor tight binding model manifesting a mobility edge protected by a duality symmetry. We propose a realistic experimental scheme to realize our results in atomic optical lattices and photonic waveguides.

5+6 pages, published version. Added a coauthor. New results on typical density of states added and revised presentation with additional supplementary information

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• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
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• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Self-consistent theory of mobility edges in quasiperiodic chains
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• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
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• Controlled charge and spin current rectifications in a spin polarized device
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• Localization to delocalization transition in a double stranded helical geometry: Effects of conformation, transverse electric field and dynamics
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Dynamical localization in non-Hermitian quasi-crystals
• Spin Localization of a Fermi Polaron in a Quasirandom Optical Lattice
• Characterization of many-body mobility edges with random matrices
• Dephasing-enhanced performance in quasiperiodic thermal machines
• Exact Mobility Edges in One-Dimensional Mosaic Lattices Inlaid with Slowly Varying Potentials