Berlin 2012 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 18: Correlated Electrons: Quantum Impurities, Kondo Physics 2

TT 18.10: Talk

Tuesday, March 27, 2012, 12:00–12:15, H 3005

Discarded weight and entanglement spectra in the numerical renormalization group — •Andreas Weichselbaum — Ludwig Maximilians University, Munich

A quantitative criterion to prove and analyze convergence within the numerical renormalization group (NRG) is introduced. By tracing out a few further NRG shells, the resulting reduced density matrices carry relevant information on numerical accuracy as well as entanglement. Their spectra can be analyzed twofold. The smallest eigenvalues provide a sensitive estimate of how much weight is discarded in the low-energy description of later iterations. As such, the discarded weight indicates in a site-specific manner 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 strong similarities with the well-known standard energy flow diagram of the NRG, supporting the prevalent usage of entanglement spectra to characterize different physical regimes [1].
Phys. Rev B 84, 125130 (2011)