Chebyshev expansion for impurity models using matrix product states

Martin Ganahl, Patrik Thunström, Frank Verstraete, Karsten Held, and Hans Gerd Evertz
Phys. Rev. B 90, 045144 – Published 30 July 2014

Abstract

We improve a recently developed expansion technique for calculating real-frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can be achieved at virtually no cost, and in sharp contrast to existing methods based on the dampening of the moments, improves the spectral resolution rather than lowering it. We validate the method for the exactly solvable resonating level model and the single impurity Anderson model. It is capable of resolving sharp Kondo resonances, as well as peaks within the Hubbard bands when employed as an impurity solver for dynamical mean-field theory. Our method works at zero temperature and allows for arbitrary discretization of the bath spectrum. It achieves similar precision as the dynamical density matrix renormalization group, at lower cost. We also propose an alternative expansion, of 1exp(τH) instead of the usual H, which opens the possibility of using established methods for the time evolution of matrix product states to calculate the spectral functions directly.

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  • Received 30 April 2014
  • Revised 15 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.045144

©2014 American Physical Society

Authors & Affiliations

Martin Ganahl1,*, Patrik Thunström2, Frank Verstraete3,4, Karsten Held2, and Hans Gerd Evertz1

  • 1Institut für Theoretische Physik, Technische Universität Graz, 8010, Graz, Austria
  • 2Institute of Solid State Physics, Vienna University of Technology, 1040, Vienna, Austria
  • 3Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
  • 4Department of Physics and Astronomy, Ghent University, Ghent, Belgium

  • *Corresponding author: martin.ganahl@gmail.com

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Vol. 90, Iss. 4 — 15 July 2014

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