The Kernel Polynomial Method

Details The Kernel Polynomial Method The Kernel Polynomial Method

2005-04-25

arxiv.org/abs/cond-mat/0504627v2

Rev. Mod. Phys. 78, 275-306 (2006)

Physics

Condensed Matter

Other Condensed Matter

32 pages, 17 figs; revised version

Scientific paper

10.1103/RevModPhys.78.275

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.

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