{
"id": "2205.06264",
"version": "v1",
"published": "2022-05-12T17:59:55.000Z",
"updated": "2022-05-12T17:59:55.000Z",
"title": "The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum",
"authors": [
"Ang-Kun Wu",
"Daniel Bauernfeind",
"Xiaodong Cao",
"Sarang Gopalakrishnan",
"Kevin Ingersent",
"J. H. Pixley"
],
"comment": "29 pages, 19 figures",
"categories": [
"cond-mat.str-el"
],
"abstract": "The Anderson model for a magnetic impurity in a one-dimensional quasicrystal is studied using the numerical renormalization group (NRG). The main focus is elucidating the physics at the critical point of the Aubry-Andre (AA) Hamiltonian, which exhibits a fractal spectrum with multifractal wave functions, leading to an AA Anderson (AAA) impurity model with an energy-dependent hybridization function defined through the multifractal local density of states at the impurity site. We first study a class of Anderson impurity models with uniform fractal hybridization functions that the NRG can solve to arbitrarily low temperatures. Below a Kondo scale $T_K$, these models approach a fractal strong-coupling fixed point where impurity thermodynamic properties oscillate with $\\log_b T$ about negative average values determined by the fractal dimension of the spectrum. The fractal dimension also enters into a power-law dependence of $T_K$ on the Kondo exchange coupling $J_K$. To treat the AAA model, we combine the NRG with the kernel polynomial method (KPM) to form an efficient approach that can treat hosts without translational symmetry down to a temperature scale set by the KPM expansion order. The aforementioned fractal strong-coupling fixed point is reached by the critical AAA model in a simplified treatment that neglects the wave-function contribution to the hybridization. The temperature-averaged properties are those expected for the numerically determined fractal dimension of $0.5$. At the AA critical point, impurity thermodynamic properties become negative and oscillatory. Under sample-averaging, the mean and median Kondo temperatures exhibit power-law dependences on $J_K$ 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.",
"revisions": [
{
"version": "v1",
"updated": "2022-05-12T17:59:55.000Z"
}
],
"analyses": {
"keywords": [
"fractal strong-coupling fixed point",
"aubry-andre anderson model",
"fractal spectrum",
"magnetic impurity",
"fractal dimension"
],
"note": {
"typesetting": "TeX",
"pages": 29,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}