The Kernel Polynomial Method

2005/04/30 by Alexander Weiße, Alexander Weisse, Gerhard Wellein +2 · 4 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Theoretical and Computational Physics #cond-mat.other #physics.comp-ph

paper · pdf · doi:10.1103/revmodphys.78.275

published as Rev. Mod. Phys. 78, 275-306 (2006) · 32 pages, 17 figs; revised version

openalex publication_date 2006/03/24 · arxiv created 2006/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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 article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. 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 we discuss in detail. In addition, we illustrate how the Kernel Polynomial Method is successfully embedded into other numerical techniques, such as Cluster Perturbation Theory or Monte Carlo simulation.

Citations

• Untersuchungen über Fouriersche Reihen
• Localization effects in quantum percolation
• Low-temperature Lanczos method for strongly correlated systems
• Spin–lattice coupling effects in the Holstein double-exchange model
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Cited by

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• Phonon spectral function of the Holstein polaron
• Real-space spectral functions of three-dimensional billion-size topological non-Hermitian matter with tensor networks
• Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube