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A quantitative criterion to prove and analyze convergence within thenumerical renormalization group (NRG) is introduced. By tracing out a fewfurther NRG shells, the resulting reduced density matrices carry relevantinformation on numerical accuracy as well as entanglement. Their spectra canthus be analyzed twofold. The smallest eigenvalues provide a sensitive estimateof how much weight is discarded in the low energy description of lateriterations. As such, the discarded weight is a clear indicator of the accuracyof a specific NRG calculation. In particular, it indicates in a site-specificmanner whether sufficiently many states have been kept within a single NRG run.The largest eigenvalues of the reduced density matrices, on the other hand,lend themselves to a straightforward analysis in terms of entanglement spectra,which can be combined into entanglement flow diagrams. The latter show strongsimilarities with the well-known standard energy flow diagram of the NRG,supporting the prevalent usage of entanglement spectra to characterizedifferent physical regimes.

Discarded weight and entanglement spectra in the Numerical Renormalization Group