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 -