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.

18 pages, 13 figures, pedagogical review

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• Localization of interacting fermions at high temperature
• Anderson localization in Bose-Einstein condensates
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Purification and many-body localization in cold atomic gases
• Dynamical localization and the effects of aperiodicity in Floquet systems
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

Cited by in corpus (3)

• Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model
• Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models