Resonant level model from a Krylov perspective: Lanczos coefficients in a quadratic model
Phys. Rev. B 113, 184301 – Published 4 May, 2026
DOI: https://doi.org/10.1103/l9zp-kg96
Abstract
We study the Lanczos coefficients in a quadratic model given by an impurity interacting with a multimode field of fermions, also known as the resonant level model. We analytically derive closed expressions for the Lanczos coefficients of Majorana fermion operators of the impurity for different structures of the coupling to the hybridization band at zero temperature. While the model remains quadratic, we find that the growth of the Lanczos coefficients structurally depends strongly on the chosen coupling. Concretely, we find (i) approximately constant, (ii) exactly constant, (iii) square-root-like, as well as (iv) linear growth in the same model. We further argue that in fact through suitably chosen couplings, essentially arbitrary Lanczos coefficients can be obtained in this model. These altogether evince the inadequacy of the Lanczos coefficients as a reliable criterion for classifying the integrability or chaoticity of the systems. Eventually, in the wideband limit, we find exponential decay of autocorrelation functions in all the settings (i)–(iv), which demonstrates the different structures of the Lanczos coefficients not being indicative of different physical behavior.
