Year: 2026
Type: article
Abstract: We study the Lanczos coefficients in a quadratic model given by an impurity interacting with a multi-mode field of fermions, also known as 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 wide-band 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.
DOI: 10.1103/l9zp-kg96
Institutions: Osnabrück University, University of Göttingen
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Awards: Korrelationen zwischen Matrixelementen von wenigteilchen Observablen in Energieeigenbasen von vielteilchen Systemen, FOR 5522: Quantenthermalisierung, Lokalisierung und eingeschränkte Dynamik mit wechselwirkenden ultrakalten Atomen, FOR 2692: Fundamental Aspects of Statistical Mechanics and the Emergence of Thermodynamics in NonEquilibrium Systems, G2744928646, G62979356
OpenAlex ID: W7154393200