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The kernel polynomial method
Open accessAbstract
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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Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
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Frigo, M., & Johnson, S. G. (2005) · Proceedings of the IEEE · doi:10.1109/jproc.2004.840301 · Cited by 5,086
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
Cited by
Time-evolution methods for matrix-product states
Paeckel, S., Köhler, T., Swoboda, A., Manmana, S. R., Schollwöck, U., & Hubig, C. (2019) · Annals of Physics · doi:10.1016/j.aop.2019.167998 · Cited by 768
Multiplet ligand-field theory using Wannier orbitals
Haverkort, M. W., Zwierzycki, M., & Andersen, O. K. (2012) · Physical Review B · doi:10.1103/physrevb.85.165113 · Cited by 444
Nearest Neighbor Tight Binding Models with an Exact Mobility Edge in One Dimension
Ganeshan, S., Pixley, J. H., & Das Sarma, S. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.146601 · Cited by 398
Electronic-structure methods for twisted moiré layers
Carr, S., Fang, S., & Kaxiras, E. (2020) · Nature Reviews Materials · doi:10.1038/s41578-020-0214-0 · Cited by 303
Single-particle excitations in disordered Weyl fluids
Pixley, J. H., Chou, Y.-Z., Goswami, P., Huse, D. A., Nandkishore, R., Radzihovsky, L., & Das Sarma, S. (2017) · Physical Review B · doi:10.1103/physrevb.95.235101 · Cited by 50
Metadata
- Authors
- Weiße, A., Wellein, G., Alvermann, A., & Fehske, H.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2006-03-24
- Volume
- 78
- Issue
- 1
- Pages
- 275-306
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2037783202
- Cited by
- 1,036
- References
- 3
- FWCI
- 7.73
- Type
- journal article
- Language
- en
- Open access
- green
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- Weiße, A., Wellein, G., Alvermann, A., & Fehske, H. (2006). The kernel polynomial method. Reviews of Modern Physics. https://doi.org/10.1103/revmodphys.78.275
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