TY - JOUR

T1 - Fractal x-ray edge problem at the critical point of the Aubry-André model

AU - Wu, Ang Kun

AU - Gopalakrishnan, Sarang

AU - Pixley, J. H.

N1 - Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/10/11

Y1 - 2019/10/11

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.100.165116

DO - 10.1103/PhysRevB.100.165116

M3 - Article

AN - SCOPUS:85074119099

SN - 2469-9950

VL - 100

JO - Physical Review B

JF - Physical Review B

IS - 16

M1 - 165116

ER -