TY - JOUR

T1 - Aubry-André Anderson model

T2 - Magnetic impurities coupled to a fractal spectrum

AU - Wu, Ang Kun

AU - Bauernfeind, Daniel

AU - Cao, Xiaodong

AU - Gopalakrishnan, Sarang

AU - Ingersent, Kevin

AU - Pixley, J. H.

N1 - Funding Information:
We thank Piers Coleman, Vladimir Dobrosavljević, Gabriel Kotliar, Johann Kroha, Andrew Millis, Qimiao Si, and Romain Vasseur for useful discussions. We are grateful to Lucy Reading-Ikkanda for creating the schematic diagrams in Fig. . A.W. and J.H.P. are partially supported by National Science Foundation (NSF) CAREER Grant No. DMR-1941569 and the Alfred P. Sloan Foundation through a Sloan Research Fellowship. S.G. acknowledges support from NSF Grant No. DMR-2103938. K.I. acknowledges support from Grant No. DMR-1508122. S.G., K.I., and J.H.P. acknowledge hospitality by the Aspen Center for Physics where part of this work was completed, and which is supported by NSF Grant No. PHY-1607611 . The authors acknowledge the following research computing resources: the Beowulf cluster at the Department of Physics and Astronomy of Rutgers University, and the Amarel cluster from the Office of Advanced Research Computing (OARC) at Rutgers, The State University of New Jersey.
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/10/15

Y1 - 2022/10/15

N2 - The interplay between incommensurability and strong correlations is a challenging open issue. It is explored here via numerical renormalization-group (NRG) study of models of a magnetic impurity in a one-dimensional quasicrystal. The principal goal is to elucidate the physics at the localization transition of the Aubry-André Hamiltonian, where a fractal spectrum and multifractal wave functions lead to a critical Aubry-André Anderson (AAA) impurity model with an energy-dependent multifractal hybridization function. This goal is reached in three stages of increasing complexity: (1) Anderson impurity models with uniform fractal hybridization functions are solved to arbitrarily low temperatures T. Below a Kondo temperature, these models approach a fractal strong-coupling fixed point where impurity thermodynamic properties are oscillatory in logbT about negative average values determined by the spectrum's fractal dimension DF<1, with b set by the fractal self-similarity near the Fermi energy. (2) An impurity hybridizing uniformly with all conduction states of the critical AAA model is shown to approach the fractal strong-coupling fixed point corresponding to DF=0.5 and b≃14. (3) When the multifractal wave functions of the critical AAA model are taken into account, low-T impurity thermodynamic properties are again negative and oscillatory, but with a more complicated structure than in (2). Under sample-averaging, the mean and median Kondo temperatures exhibit power-law dependencies on the Kondo coupling with exponents characteristic of different fractal dimensions. We attribute these signatures to the impurity probing a distribution of fractal strong-coupling fixed points with decreasing temperature. To treat the AAA model, the numerical renormalization group (NRG) is combined with the kernel polynomial method (KPM) to form a general, efficient treatment of hosts without translational symmetry in arbitrary dimensions down to a temperature scale set by the KPM expansion order. Implications of our results for heavy-fermion quasicrystals and other applications of the NRG+KPM approach are discussed.

AB - The interplay between incommensurability and strong correlations is a challenging open issue. It is explored here via numerical renormalization-group (NRG) study of models of a magnetic impurity in a one-dimensional quasicrystal. The principal goal is to elucidate the physics at the localization transition of the Aubry-André Hamiltonian, where a fractal spectrum and multifractal wave functions lead to a critical Aubry-André Anderson (AAA) impurity model with an energy-dependent multifractal hybridization function. This goal is reached in three stages of increasing complexity: (1) Anderson impurity models with uniform fractal hybridization functions are solved to arbitrarily low temperatures T. Below a Kondo temperature, these models approach a fractal strong-coupling fixed point where impurity thermodynamic properties are oscillatory in logbT about negative average values determined by the spectrum's fractal dimension DF<1, with b set by the fractal self-similarity near the Fermi energy. (2) An impurity hybridizing uniformly with all conduction states of the critical AAA model is shown to approach the fractal strong-coupling fixed point corresponding to DF=0.5 and b≃14. (3) When the multifractal wave functions of the critical AAA model are taken into account, low-T impurity thermodynamic properties are again negative and oscillatory, but with a more complicated structure than in (2). Under sample-averaging, the mean and median Kondo temperatures exhibit power-law dependencies on the Kondo coupling with exponents characteristic of different fractal dimensions. We attribute these signatures to the impurity probing a distribution of fractal strong-coupling fixed points with decreasing temperature. To treat the AAA model, the numerical renormalization group (NRG) is combined with the kernel polynomial method (KPM) to form a general, efficient treatment of hosts without translational symmetry in arbitrary dimensions down to a temperature scale set by the KPM expansion order. Implications of our results for heavy-fermion quasicrystals and other applications of the NRG+KPM approach are discussed.

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U2 - 10.1103/PhysRevB.106.165123

DO - 10.1103/PhysRevB.106.165123

M3 - Article

AN - SCOPUS:85141263656

SN - 2469-9950

VL - 106

JO - Physical Review B

JF - Physical Review B

IS - 16

M1 - 165123

ER -