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Quantum Monte Carlo simulations of solids
Abstract
This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic wave-function-based approaches provide a very direct treatment of quantum many-body effects and serve as benchmarks against which other techniques may be compared. They complement the less demanding density-functional approach by providing more accurate results and a deeper understanding of the physics of electronic correlation in real materials. The algorithms are intrinsically parallel, and currently available high-performance computers allow applications to systems containing a thousand or more electrons. With these tools one can study complicated problems such as the properties of surfaces and defects, while including electron correlation effects with high precision. The authors provide a pedagogical overview of the techniques and describe a selection of applications to ground and excited states of solids and clusters.
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Cites
Special points for Brillouin-zone integrations
Monkhorst, H. J., & Pack, J. D. (1976) · Physical Review B · doi:10.1103/physrevb.13.5188 · Cited by 71,721
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Self-interaction correction to density-functional approximations for many-electron systems
Perdew, J. P., & Zunger, A. (1981) · Physical Review B · doi:10.1103/physrevb.23.5048 · Cited by 20,887
�ber die Quantenmechanik der Elektronen in Kristallgittern
Bloch, F. (1929) · Zeitschrift f�r Physik · doi:10.1007/bf01339455 · Cited by 3,436
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Saal, J. E., Kirklin, S., Aykol, M., Meredig, B., & Wolverton, C. (2013) · JOM · doi:10.1007/s11837-013-0755-4 · Cited by 2,584
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Hautier, G., Ong, S. P., Jain, A., Moore, C. J., & Ceder, G. (2012) · Physical Review B · doi:10.1103/physrevb.85.155208 · Cited by 506
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Stoudenmire, E. M., & White, S. R. (2012) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-020911-125018 · Cited by 451
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Lin, C., Zong, F. H., & Ceperley, D. M. (2001) · Physical Review E · doi:10.1103/physreve.64.016702 · Cited by 371
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Santoro, G. E., & Tosatti, E. (2006) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/39/36/r01 · Cited by 354
Johnson, T. H., Clark, S. R., & Jaksch, D. (2014) · EPJ Quantum Technology · doi:10.1140/epjqt10 · Cited by 127
Haegeman, J., & Verstraete, F. (2017) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031016-025507 · Cited by 118
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The Shape of Full Configuration Interaction to Come
Eriksen, J. J. (2021) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.0c03225 · Cited by 66
Computational complexity in electronic structure
Whitfield, J. D., Love, P. J., & Aspuru-Guzik, A. (2013) · Phys. Chem. Chem. Phys. · doi:10.1039/c2cp42695a · Cited by 71
Qin, M., Shi, H., & Zhang, S. (2016) · Physical Review B · doi:10.1103/physrevb.94.235119 · Cited by 58
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Metadata
- Authors
- Foulkes, W. M. C., Mitas, L., Needs, R. J., & Rajagopal, G.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2001-01-05
- Volume
- 73
- Issue
- 1
- Pages
- 33-83
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2072808339
- Cited by
- 2,336
- References
- 5
- FWCI
- 30.17
- Type
- journal article
- Language
- en
- Open access
- closed
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