Tensor networks and the numerical renormalization group

Andreas Weichselbaum
Phys. Rev. B 86, 245124 – Published 20 December 2012

Abstract

The full-density-matrix numerical renormalization group has evolved as a systematic and transparent setting for the calculation of thermodynamical quantities at arbitrary temperatures within the numerical renormalization group (NRG) framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets introduced by Anders and Schiller [Phys. Rev. Lett. 95, 196801 (2005)]. In addition, specific attention is given to the possible feedback from low-energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-golden-rule calculations (fgrNRG) as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.

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  • Received 14 September 2012

DOI:https://doi.org/10.1103/PhysRevB.86.245124

©2012 American Physical Society

Authors & Affiliations

Andreas Weichselbaum

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

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Vol. 86, Iss. 24 — 15 December 2012

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