Accuracy of the typicality approach using Chebyshev polynomials-Reference-Cited by-同舟云学术

Accuracy of the typicality approach using Chebyshev polynomials

Published:2021-06-21 Issue:9 Volume:76 Page:823-834
ISSN:0932-0784
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Schlüter Henrik¹,Gayk Florian¹,Schmidt Heinz-Jürgen²^ORCID,Honecker Andreas³^ORCID,Schnack Jürgen¹^ORCID

Affiliation:

1. Fakultät für Physik , Universität Bielefeld , Postfach 100131 , Bielefeld D-33501 , Germany

2. Fachbereich Physik , Universität Osnabrück , Osnabrück D-49069 , Germany

3. Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089 , CY Cergy Paris Université , Cergy-Pontoise Cedex F-95302 , France

Abstract

Abstract Trace estimators allow us to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples.

Publisher

Walter de Gruyter GmbH

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/zna-2021-0116/pdf

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