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We propose an auxiliary-bath algorithm for the numerical renormalizationgroup (NRG) method to solve multi-impurity models with shared electron baths.The method allows us to disentangle the electron baths into independent Wilsonchains to perform standard NRG procedures beyond the widely adopted independentbath approximation. Its application to the 2-impurity model immediatelyreproduces the well-known even- and odd-parity channels. For 3-impurity Kondomodels, we find successive screening of collective degrees of freedom such asthe helicity and the cluster spin, and clarify the false prediction of anon-Fermi liquid ground state in unphysical parameter region in previousliterature due to improper treatment of disentanglement. Our work highlightsthe importance of nonlocal spatial correlations due to shared baths and revealsa generic picture of successive collective screening for the entropy depletionthat is crucial in real correlated systems. Our method greatly expands theapplicability of the NRG and opens an avenue for its further development.

Auxiliary-Bath Numerical Renormalization Group Method and Successive Collective Screening in Multi-Impurity Kondo Systems