Critical eigenstates and their properties in one and two dimensional quasicrystals

Abstract

We present exact solutions for some eigenstates of hopping models on one and two dimensional quasiperiodic tilings and show that they are "critical" states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement.

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• Exact relations between multifractal exponents at the Anderson transition
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Analytical results for Scaling Properties of the Spectrum of the Fibonacci Chain
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• Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling
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• Electrons in deterministic quasicrystalline potentials and hidden conserved quantities
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Cited by in corpus (44)

• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Conventional superconductivity in quasicrystals
• Many-body localization in a quasiperiodic Fibonacci chain
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
• Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
• Strictly localized states in the octagonal Ammann-Beenker quasicrystal
• Quantum phase transition between hyperuniform density distributions
• Landau levels in quasicrystals
• Nature of Protected Zero Energy States in Penrose Quasicrystals
• The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring
• Length scale formation in the Landau levels of quasicrystals
• Intrinsic vortex pinning in superconducting quasicrystals
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems
• Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals
• Hyperuniform electron distributions controlled by electron interactions in quasicrystal
• Josephson effect in a Fibonacci quasicrystal
• Perpendicular space accounting of localized states in a quasicrystal
• Topological critical states and anomalous electronic transmittance in one dimensional quasicrystals
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Topological superconductivity in Fibonacci quasicrystals
• Electronic states of a disordered 2D quasiperiodic tiling: from critical states to Anderson localization
• Quasiperiodic criticality and spin-triplet superconductivity in superconductor-antiferromagnet moire patterns
• Properties of the Ammann-Beenker tiling and its square approximants
• Fractalized magnon transport on the quasicrystal with enhanced stability
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
• Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing
• Level-spectra Statistics in Planar Fractal Tight-Binding Models
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Multifractality and Hyperuniformity in Quasicrystalline Bose-Hubbard Models with and without Disorder
• Optical observation of quasiperiodic Heisenberg antiferromagnets in two dimensions
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Hidden hyperspace geometry and long-distance quantum coupling
• Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice
• Determination of the Electronic Localized-to-Extended-State Transition Point around the Metal-to-Insulator Transition Region of Fluid Mercury Using the Framework of Multifractal Analysis
• Optical response of the tightbinding model on the Fibonacci chain
• Superconducting order parameter in aperiodic binary systems
• Modulated honeycomb lattices and their magnetic properties