The Aubry-André model as the hobbyhorse for understanding localization phenomenon

Abstract

We present a thorough pedagogical analysis of the single particle localization phenomenon in a quasiperiodic lattice in one dimension. Description of disorder in the lattice is represented by the Aubry-André model. Characterization of localization is performed through the analysis of both, stationary and dynamical properties. The stationary properties investigated are the inverse participation ratio (IPR), the normalized participation ratio (NPR) and the energy spectrum as a function of the disorder strength. As expected, the distinctive Hofstadter pattern is found. Two dynamical quantities allow discerning the localization phenomenon, being the spreading of an initially localized state and the evolution of population imbalance in even and odd sites across the lattice.

arXiv comment18 pages, 13 figures, pedagogical review

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• Ergodicity breaking in an incommensurate system observed by OTOCs and Loschmidt Echoes: From quantum diffusion to sub-diffusion
• A numerical study of the localization transition of Aubry-André type models
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• Entropy of the quantum work distribution
• Dynamical transitions in aperiodically kicked tight-binding models
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• Flux enhanced localization and reentrant delocalization in the quench dynamics of two interacting bosons on a Bose-Hubbard ladder
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• Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
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• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Bound states in one-dimensional systems with colored noise
• Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
• Gauge fields induced by curved spacetime
• Disorder driven topological phase transitions in 1D mechanical quasicrystals
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Persistent revivals in a system of trapped bosonic atoms
• Characterizing the delocalized-localized Anderson phase transition based on the system's response to boundary conditions
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Localization transitions in quadratic systems without quantum chaos
• Quantum walkers in a disordered lattice with power-law hopping
• From generating functions to the geometric Binder cumulant
• Inverse determination of light-matter coupling in disordered systems from transmittance spectra
• Parametrized Version of the Generalized Aubry-André Model
• Phase Transitions and Critical Behavior in Quasi-One-Dimensional Two-Channel Systems with Quasiperiodic Disorder
• Charge current and phase diagram of the disordered open longer-range Kitaev chain
• Quantum localization in incommensurate tight-binding chains