The Kondo screening of a localized magnetic moment crucially depends on the spectral properties of the electronic bath to which it is coupled. Unlike textbook examples, realistic systems as well as dynamical mean-field theory of correlated lattice models force us to consider sharp features in the hybridization function near the Fermi energy. Divergencies of this kind can play a relevant role in twisted bilayer graphene, for which local-moment formation and isospin entropy at finite temperature are currently under the spotlight. We clarify how a low-frequency singularity impacts the screening mechanisms by means of a toy model with a tunable $\delta$ peak in the hybridization function, superimposed to a regular part. Our analysis unveils an unexpectedly big impact on the local-moment physics already for a parametrically small weight of the flat band in the bath.

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• Kondo effect
• Anderson impurity model
• Quantum Monte Carlo
• Renormalization group