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.

References in corpus (4)

• Exact relations between multifractal exponents at the Anderson transition
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings
• Generalized Inverse Participation Numbers in Metallic-Mean Quasiperiodic Systems

Cited by in corpus (10)

• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Conventional superconductivity in quasicrystals
• Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
• Quantum phase transition between hyperuniform density distributions
• Nature of Protected Zero Energy States in Penrose Quasicrystals
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Fractalized magnon transport on the quasicrystal with enhanced stability
• Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing
• Optical response of the tightbinding model on the Fibonacci chain