Fractal x-ray edge problem at the critical point of the Aubry-André model

Abstract

We study the Anderson orthogonality catastrophe, and the corresponding x-ray edge problem, in systems that are at a localization transition driven by a deterministic quasiperiodic potential. Specifically, we address how the ground state of the Aubry-Andre model, at its critical point, responds to an instantaneous local quench. At this critical point, both the single-particle wavefunctions and the density of states are fractal. We find, numerically, that the overlap between post-quench and pre-quench wavefunctions, as well as the "core-hole" Green function, evolve in a complex, non-monotonic way with system size and time respectively. We interpret our results in terms of the fractal density of states at this critical point. In a given sample, as the post-quench time increases, the system resolves increasingly finely spaced minibands, leading to a series of alternating temporal regimes in which the response is flat or algebraically decaying. In addition, the fractal critical wavefunctions give rise to a quench response that varies strongly from site to site across the sample, which produces broad distributions of many-body observables. Upon averaging this broad distribution over samples, we recover coarse-grained power laws and dynamical exponents characterizing the x-ray edge singularity. We discuss how these features can be probed in ultra-cold atomic gases using radio-frequency spectroscopy and Ramsey interference.

arXiv comment12 pages, 10 figures

References in corpus (22)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Bosonization and Strongly Correlated Systems
• Bose-Einstein condensation of atoms in a uniform potential
• Quantum critical state in a magnetic quasicrystal
• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• Non-local Adiabatic Response of a Localized System to Local Manipulations
• Interacting fermions in self-similar potentials
• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments
• Logarithmic Entanglement Lightcone in Many-Body Localized Systems
• Non-power-law universality in one-dimensional quasicrystals
• Long-range Magnetic Order in Models for Rare Earth Quasicrystals
• Shifts of Random Energy Levels by a Local Perturbation
• Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems
• Anderson Orthogonality Catastrophe in Disordered Systems
• Kondo-Anderson Transitions
• Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals
• Multifractal Orthogonality Catastrophe in 1D Random Quantum Critical Points
• A Kondo impurity in a disordered metal: Anderson's theorem revisited

Cited by in corpus (4)

• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe