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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