Variational matrix-product-state approach to quantum impurity models

A. Weichselbaum, F. Verstraete, U. Schollwöck, J. I. Cirac, and Jan von Delft
Phys. Rev. B 80, 165117 – Published 13 October 2009

Abstract

We present a unified framework for renormalization group methods, including Wilson’s numerical renormalization group (NRG), and White’s density-matrix renormalization group (DMRG), within the language of matrix-product-states. This allows improvements over Wilson’s NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green’s functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially linear scaling of complexity for n-channel problems.

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  • Received 25 August 2008

DOI:https://doi.org/10.1103/PhysRevB.80.165117

©2009 American Physical Society

Authors & Affiliations

A. Weichselbaum1, F. Verstraete2, U. Schollwöck1, J. I. Cirac3, and Jan von Delft1

  • 1Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität München, 80333 Munich, Germany
  • 2Institut der Theoretischen Physik, Universität Wien, Boltzmanngasse 3, A-1090 Vienna, Austria
  • 3Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, Garching D-85748, Germany

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Vol. 80, Iss. 16 — 15 October 2009

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