The Anderson impurity problem in a multifractal host

ORAL

Abstract

We present results of a numerical study of the single-impurity Anderson problem in a one-dimensional quasicrystal described by the Aubry-Andre (AA) model. The AA model exhibits an Anderson localization transition at a critical value of the incommensurate potential strength. At the critical point, the impurity hybridizes with the electrons through the local density of states (LDOS) based on the fractal spectrum (a non-uniform Cantor set) and multifractal wavefunctions. The complexity of the resulting Anderson impurity problem can be attributed to the multi-scaling from the multifractal LDOS over different ranges of energy and temperature. For these systems lacking translation symmetry, we combine the kernel polynomial method (KPM) with the numerical renormalization group (NRG) to efficiently obtain the parameters of the tight-binding Wilson chain without the need for any integration. We benchmark this KPM+NRG approach against the density matrix renormalization group in their regime of mutual applicability. We present and interpret low-temperature thermodynamic properties.

*NSF CAREER Grant No. DMR1941569 and the Alfred P. Sloan Foundation through a Sloan Research Fellowship.

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Presenters

  • Kevin Ingersent

    • University of Florida

Authors

  • Angkun Wu

    • Rutgers University
    • Department of Physics and Astronomy, Center for Materials Theory,Rutgers University, Piscataway, New Jersey 08854, USA

  • Daniel Bauernfeind

    • Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
    • Simons Foundation

  • Xiaodong Cao

    • Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA

  • Andrew J Millis

    • Columbia University
    • Columbia University; Flatiron Institute
    • Columbia University, Flatiron Institute

  • Sarang Gopalakrishnan

    • Pennsylvania State University
    • Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314, USA
    • Penn State

  • Kevin Ingersent

    • University of Florida

  • Jed Pixley

    • Rutgers University