The Kondo effect is a hallmark of strongly correlated systems, where an impurity's local degrees of freedom are screened by conduction electrons, forming a many-body singlet. With increasing degrees of freedom in the impurity, theoretical studies face significant challenges in accurately identifying and characterizing the underlying mechanisms that screen the impurity. In this work, we introduce a straightforward yet powerful methodology for identifying the formation of Kondo singlets and their screening mechanisms, by utilizing the numerical renormalization group combined with the matrix product states technique. We demonstrate the effectiveness of our method on the single and two-level Anderson impurity models. Furthermore, we outline generalizations to multichannel and multiorbital Kondo impurities, showing how advanced tensor network techniques render our approach a versatile framework for tackling complex impurity systems.

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• Kondo effect
• Matrix product states
• Multichannel Anderson model
• Numerical Renormalization Group