The Anderson impurity problem in a multifractal host*

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.