The kernel polynomial method
By A. Weisse, G. Wellein, Andreas Alvermann, H. Fehske. 2005
815 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/23eb9f2695b9df49ea2f11fd60e2978b975ea1a7
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In Atomic and Molecular Physics, and Optics
- Jeffrey Pennington
- A. Alexandrov
- Y. Saad
- Lin Lin
- J. Devreese
- Valeria Simoncini
- Michele Benzi
- Krishnan Suresh
In Condensed Matter Physics
Citations in the corpus
- Detection of Kardar–Parisi–Zhang hydrodynamics in a quantum Heisenberg spin-1/2 chain (2020, neutral): “[18] Prosen, T.”
- Approximating Spectral Densities of Large Matrices (2013, positive): “The method, which is widely used in a variety of calculations that require the DOS [13], has continued to receive a tremendous amount of interest in the last few years [13, 6, 25, 38].”
- Estimating the Spectral Density of Large Implicit Matrices (2018, methodology): “See Weiße et al. (2006) for a review of the kernel polynomial method and a broader historical perspective on these estimation techniques in physics and quantum chemistry.”
- Fröhlich polaron and bipolaron: recent developments (2009, methodology): “More recent ED, VED and a kernel polynomial method (KPM) (for a review of KPM see (Weiße et al. , 2006)) allowed for numerical calculations of lattice polaron properties in the Holstein model in the whole parameter range on fairly large systems (Barisic , 2004; El Shawish et al. , 2003; Schubert et…”