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The kernel polynomial method

Alexander Weiße*, Gerhard Wellein, Andreas Alvermann, and Holger Fehske

Alexander Weiße*

  • School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia

Gerhard Wellein

  • Regionales Rechenzentrum Erlangen, Universität Erlangen, D-91058 Erlangen, Germany

Andreas Alvermann and Holger Fehske

  • Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, D-17487 Greifswald, Germany

  • *Present address: Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, D-17487 Greifswald, Germany.
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Rev. Mod. Phys. 78, 275 – Published 24 March, 2006

DOI: https://doi.org/10.1103/RevModPhys.78.275

Abstract

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed-matter physics. In this paper basic properties and recent developments of Chebyshev expansion based algorithms and the kernel polynomial method are reviewed. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad application not only in physics. Representative examples from the fields of disordered systems, strongly correlated electrons, electron-phonon interaction, and quantum spin systems are discussed in detail. In addition, an illustration on how the kernel polynomial method is successfully embedded into other numerical techniques, such as cluster perturbation theory or Monte Carlo simulation, is provided.

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Rev. Mod. Phys. 78, 275– Published 24 March, 2006

    © 2006 American Physical Society

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