Discarded weight and entanglement spectra in the numerical renormalization group

A. Weichselbaum
Phys. Rev. B 84, 125130 – Published 16 September 2011

Abstract

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 16 June 2011

DOI:https://doi.org/10.1103/PhysRevB.84.125130

©2011 American Physical Society

Authors & Affiliations

A. Weichselbaum

  • Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität, D-80333 Munich, Germany

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 84, Iss. 12 — 15 September 2011

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×