Critical phase dualities in 1D exactly-solvable quasiperiodic models

Abstract

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of PRL 114, 146601 and PRL 104, 070601. The analytical treatment follows from recognizing these models as a novel type of fixed-points of the renormalization group procedure recently proposed in arXiv:2206.13549 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and non-trivial mobility edges without the need for the unbounded potentials required by previous proposals.

arXiv admin note: text overlap with arXiv:2206.13549

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Cited by in corpus (43)

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• Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
• Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• A numerical study of the localization transition of Aubry-André type models
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Effective delocalization in the one-dimensional Anderson model with stealthy disorder
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Multifractality in monitored single-particle dynamics
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder
• Structural constraints on mobility edges in one-dimensional quasiperiodic systems
• Experimental observation of exact quantum critical states
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Quasiperiodic Quadrupole Insulators
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Fate of Quadratic Band Crossing under quasiperiodic modulation
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Family of self-dual quasicrystals with critical Phases
• Fractal Quasicondensation in One Dimension
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal