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

Ang Kun Wu, Sarang Gopalakrishnan, J. H. Pixley

Research output: Contribution to journalArticlepeer-review

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-André model, at its critical point, responds to an instantaneous local quench. At this critical point, both the single-particle wave functions and the density of states are fractal. We find, numerically, that the overlap between postquench and prequench wave functions, as well as the "core-hole" Green function, evolve in a complex, nonmonotonic 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 postquench 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 wave functions 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 ultracold atomic gases using radio-frequency spectroscopy and Ramsey interference.

Original languageEnglish (US)
Article number165116
JournalPhysical Review B
Volume100
Issue number16
DOIs
StatePublished - Oct 11 2019

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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