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8 - Quantum Monte Carlo methods

Published online by Cambridge University Press:  24 November 2021

David Landau  and
Kurt Binder
David Landau
Affiliation:
University of Georgia
Kurt Binder
Affiliation:
Johannes Gutenberg Universität Mainz, Germany
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Summary

In most of the discussion presented so far in this book, the quantum character of atoms and electrons has been ignored. The Ising spin models have been an exception, but since the Ising Hamiltonian is diagonal (in the absence of a transverse magnetic field), all energy eigenvalues are known and the Monte Carlo sampling can be carried out just as in the case of classical statistical mechanics. Furthermore, the physical properties are in accord with the third law of thermodynamics for Ising-type Hamiltonians (e.g. entropy S and specific heat vanish for temperature T → 0, etc.) in contrast to the other truly classical models dealt with in previous chapters (e.g. classical Heisenberg spin models, classical fluids and solids, etc.) which have many unphysical low temperature properties.

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A Guide to Monte Carlo Simulations in Statistical Physics , pp. 365 - 415
Publisher: Cambridge University Press
Print publication year: 2021

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References

Abanov, A. and Chubukov, A. V. (2000), Phys. Rev. Lett. 84, 5608.Google Scholar
Abanov, A. and Chubukov, A. V. (2004), Phys. Rev. Lett. 93, 255702.CrossRefGoogle Scholar
Anderson, J. B. (1975), J. Chem. Phys. 63, 1499Google Scholar
Assaad, F. F. and Evertz, H. G. (2008), Computational Many-Particle Physics, Lecture Notes in Physics (Springer, Berlin), p. 739.Google Scholar
Badinski, A. and Needs, R. J. (2007), Phys. Rev. E 76, 036707.CrossRefGoogle Scholar
Barma, M. and Shastry, B. S. (1977), Phys. Lett. 61A, 15.CrossRefGoogle Scholar
Barma, M. and Shastry, B. S. (1978), Phys. Rev. B 18, 3351.CrossRefGoogle Scholar
Batchelder, D. N., Losee, D. L., and Simmons, R. O. (1968), Phys. Rev. 73, 873.Google Scholar
Beard, B. B. and Wiese, U.-J. (1996), Phys. Rev. Lett. 77, 5130.Google Scholar
Berg, E., Metlitski, M. A., and Sachdev, S. (2012), Science 338, 1606.Google Scholar
Berne, B. J. and Thirumalai, D. (1986), Ann. Rev. Phys. Chem. 37, 401.Google Scholar
Bethe, H. A. (1931), Z. Phys. 71, 205.Google Scholar
Blanckenbecler, R., Scalapino, D. J., and Sugar, R. L. (1981), Phys. Rev. D 24, 2278.Google Scholar
Boninsegni, M., Prokof’ev, N., and Svistunov, B. (2006a), Phys. Rev. E 74, 036701.CrossRefGoogle Scholar
Boninsegni, M., Prokof’ev, N., and Svistunov, B. (2006b), Phys. Rev. Lett. 96, 070601.Google Scholar
Bonner, J. C. and Fisher, M. E. (1964), Phys. Rev. 135, A640.Google Scholar
Booth, G. H., Grüneis, A., Kresse, G., and Alavi, A. (2012), Nature 493, 465.Google Scholar
Booth, G. H., Thorn, A. J. W., and Alavi, A. (2009), J. Chem. Phys. 131, 054106.Google Scholar
Carlson, J., Gandolfi, S., Pieper, S. C., Schmidt, K. E., and Wiringa, R. B. (2015), Rev. Mod. Phys. 87, 1067.CrossRefGoogle Scholar
Ceperley, D. M. (1995), Rev. Mod. Phys. 67, 279.Google Scholar
Ceperley, D. M. (1996), in Monte Carlo and Molecular Dynamics of Condensed Matter Systems, eds. Binder, K. and Ciccotti, G. (Societá Italiana di Fisica, Bologna), p. 445.Google Scholar
Ceperley, D. M. and Alder, B. J. (1980), Phys. Rev. Lett. 45, 566.Google Scholar
Ceperley, D. M. and Kalos, M. H. (1979), Monte Carlo Methods in Statistical Physics, ed. Binder, K. (Springer, Berlin), p. 145.Google Scholar
Cizek, J. (1966), J. Chem. Phys. 49, 4256.Google Scholar
Cleland, D., Booth, G. H., and Alavi, A. (2010), J. Chem. Phys. 132, 041103.Google Scholar
Cleland, D., Booth, G. H., Overy, C., and Alavi, A. (2012), J. Chem. Theory Comput. 8, 4138.CrossRefGoogle Scholar
Cohen, A. J., Mon-Sanchez, M., and Yang, W. (2012), Chem. Rev. 112, 189.Google Scholar
Cullen, J. J. and Landau, D. P. (1983), Phys. Rev. B. 27, 297.Google Scholar
Dadobaev, G. and Slutsker, A. I. (1981), Soviet Phys. Solid State 23, 1131.Google Scholar
de Raedt, H. and Lagendijk, A. (1981), Phys. Rev. Lett. 46, 77.Google Scholar
de Raedt, H. and Lagendijk, A. (1985), Phys. Rep. 127, 233.Google Scholar
de Raedt, H. and von der Linden, W. (1992), in The Monte Carlo Method in Condensed Matter Physics, ed. Binder, K. (Springer, Berlin), p. 249.Google Scholar
Doll, J. D. and Gubernatis, J. E. (eds.) (1990), Quantum Simulations (World Scientific, Singapore).Google Scholar
Doniach, S., Iuni, M., Kalmeyer, V., and Gabay, M. (1988), Europhys. Lett. 6, 663.Google Scholar
Evertz, H. G. and Marcu, M. (1993), in Computer Simulations Studies in Condensed Matter Physics VI, eds. Landau, D. P., Mon, K. K., and Schüttler, H.-B. (Springer, Heidelberg), p. 109.Google Scholar
Evertz, H. G., Lana, G., and Marcu, M. (1993), Phys. Rev. Lett. 70, 875.Google Scholar
Ewald, P. (1921), Ann. Phys. 74, 253.Google Scholar
Feynman, R. P. (1953), Phys. Rev. 90, 1116; 91, 1291; 91, 1301.Google Scholar
Feynman, R. P. and Hibbs, A. R. (1965), Quantum Mechanics and Path Integrals (McGraw Hill, New York).Google Scholar
Foulkes, M. W. C., Mitas, L., Needs, R. J., and Rajagopal, G. (2001), Rev. Mod. Phys. 73, 33.Google Scholar
Gandolfi, S., Carlson, J., and Reddy, S. (2012), Phys. Rev. C 85, 032801.CrossRefGoogle Scholar
Gandolfi, S., Lovato, A., Carlson, J., and Schmidt, K. E. (2014), Phys. Rev. C 90, 061306.Google Scholar
Gezerlis, A., Tews, I., Epelbaum, E., Freunek, M., Gandolfi, S., Hebeler, K., Nogga, A., and Schwenk, A. (2014). Phys. Rev. C 90, 054323.Google Scholar
Gillan, M. J. and Christodoulos, F. (1993), Int. J. Mod. Phys. C4, 287.Google Scholar
Gomez-Santos, G. Joannopoulos, J. D., and Negele, J. W. (1989), Phys. Rev. B 39, 4435.Google Scholar
Grossman, J. C. and Mitas, L. (2005), Phys. Rev. Lett. 94, 056403.Google Scholar
Gubernatis, J. E. and Kawashima, N. (1996), in Monte Carlo and Molecular Dynamics of Condensed Matter Systems, eds. Binder, K. and Ciccotti, G. (Societa Italiana di Fisica, Bologna), p. 519.Google Scholar
Gubernatis, J., Kawashima, N., and Philipp, W. (2016), Quantum Monte Carlo Methods: Algorithms for Lattice Models (Cambridge University Press, Cambridge).CrossRefGoogle Scholar
Gubernatis, J. E., Jarrell, M., Silver, R. N., and Sivia, D. S. (1991), Phys. Rev. B 44, 6011.Google Scholar
Gull, E., Millis A, J., Lichtenstein, A. I., Rubtsov, A. N., Troyer, M., and Werner, P. (2011), Rev. Mod. Phys. 83, 349.Google Scholar
Handscomb, D. C. (1962), Proc. Cambridge Philos. Soc. 58, 594.CrossRefGoogle Scholar
Handscomb, D. C. (1964), Proc. Cambridge Philos. Soc. 60, 115.CrossRefGoogle Scholar
Hirsch, J. E., Sugar, R. L., Scalapino, D. J., and Blancenbecler, R. (1982), Phys. Rev. B 26, 5033.Google Scholar
Homma, S., Matsuda, H., and Ogita, N. (1984), Prog. Theor. Phys. 72, 1245.Google Scholar
Homma, S., Matsuda, H., and Ogita, N. (1986), Prog. Theor. Phys. 75, 1058.Google Scholar
Horsch, R. and von der Linden, W. (1988), Z. Phys. B 72, 181.Google Scholar
Hubbard, J. (1963), Proc. Roy. Soc. London A 276, 238.Google Scholar
Hulthén, J. L. (1938), Ark. Mat. Astron. Fjs. A 26, 1.Google Scholar
Huse, D. A. and Elser, V. (1988), Phys. Rev. Lett. 60, 2531.Google Scholar
Kalos, M. H. (ed.) (1984), Monte Carlo Methods in Quantum Problems (D. Reidel, Dordrecht).Google Scholar
Kasteleijn, P. W. (1952), Physica 18, 104.Google Scholar
Kawashima, N. (1997), in Computer Simulations Studies in Condensed Matter Physics IX, eds. Landau, D. P., Mon, K. K., and Schüttler, H.-B. (Springer, Heidelberg), p. 45.Google Scholar
Kawashima, N. and Gubernatis, J. E. (1995), Phys. Rev. E 51, 1547.Google Scholar
Kohn, W. (1999), Rev. Mod. Phys. 71, 1253.Google Scholar
Lee, D. H., Joannopoulos, J. D., and Negele, J. W. (1984), Phys. Rev. B 30, 1599.Google Scholar
Liang, S., Doucot, B., and Anderson, P. W. (1988), Phys. Rev. Lett. 61, 365.Google Scholar
Loewdin, P. O. (1955), Phys. Rev. 97, 1474.Google Scholar
Loh, E. Y., Gubernatis, J. E., Scalettar, R. T., White, S. R., Scalapino, D. J., and Sugar, R. L. (1990), Phys. Rev. B 41, 9301.CrossRefGoogle Scholar
Lopez-Rios, P., Ma, A., Drummond, N. D., Fowler, M. D., and Needs, R. J. (2006), Phys. Rev. E 74, 066701.Google Scholar
Lovato, A., Gandolfi, S., Butler, R., Carlson, J., Lusk, E., Pieper, S. C., and Schiavilla, R. (2013), Phys. Rev. Lett. 111, 092501.Google Scholar
Lyklema, J. W. (1982), Phys. Rev. Lett. 49, 88.Google Scholar
Manousakis, E. and Salvador, R. (1989), Phys. Rev. B 39, 575.Google Scholar
Marinari, E. and Parisi, G. (1992), Europhys. Lett. 19, 451.Google Scholar
Marshall, W. (1955), Proc. Roy. Soc. London A 232, 64.Google Scholar
Martonak, P., Paul, W., and Binder, K. (1998), Phys. Rev. E 57, 2425.CrossRefGoogle Scholar
Marx, D. and Nielaba, P. (1992), Phys. Rev. A 45, 8968.Google Scholar
Marx, D. and Wiechert, H. (1996), Adv. Chem. Phys. 95, 213.Google Scholar
Marx, D., Opitz, O., Nielaba, P., and Binder, K. (1993), Phys. Rev. Lett. 70, 2908.Google Scholar
Metlitski, M. A., and Sachdev, S. (2010), Phys. Rev. B 82, 075128.Google Scholar
Miyazawa, S. and Homma, S. (1995), in Computer Simulations Studies in Condensed Matter Physics VIII, eds. Landau, D. P., Mon, K. K., and Schüttler, H.-B. (Springer, Heidelberg), p. 78.Google Scholar
Miyazawa, S., Miyashita, S., Makivic, M. S., and Homma, S. (1993), Prog. Theor. Phys. 89, 1167.CrossRefGoogle Scholar
Møller, C. and Plesset, M. S. (1934), Phys. Rev. 46, 618.CrossRefGoogle Scholar
Müser, M. H. (1996), Mol. Simulation 17, 131.Google Scholar
Müser, M. H., Nielaba, P., and Binder, K. (1995), Phys. Rev. B 51, 2723.Google Scholar
Nho, K. and Landau, D. P. (2004), Phys. Rev. A 70, 053614.Google Scholar
Nielaba, P. (1997), in Annual Reviews of Computational Physics V, ed. Stauffer, D. (World Scientific, Singapore), p. 137.Google Scholar
Okabe, Y. and Kikuchi, M. (1986), Phys. Rev. B 34, 7896.Google Scholar
Onsager, L. (1944), Phys. Rev. 65, 117.Google Scholar
Ovchinnikov, A. A. (1973), Sov. Phys. JETP 37, 176.Google Scholar
Pople, J. A. (1999), Rev. Mod. Phys. 71, 1267.Google Scholar
Raghavachari, K., Trucks, G. W., Pople, J. A., and Head-Gordon, M. (1989), Chem. Phys. Lett. 157, 479.Google Scholar
Reger, J. D. and Young, A. P. (1988), Phys. Rev. B 37, 5978.Google Scholar
Rutledge, G. C., Lacks, D. J., Martonak, R., and Binder, K. (1998), J. Chem. Phys. 108, 10274.Google Scholar
Sandvik, A. W. (1992), J. Phys. A 25, 3667.Google Scholar
Sandvik, A. W. (1997), Phys. Rev. B 56, 14510.Google Scholar
Sandvik, A. W. (1998), Phys. Rev. Lett. 80, 5196.Google Scholar
Sandvik, A. W. and Kurkijärvi, J. (1991), Phys. Rev. B 43, 5950.Google Scholar
Schattner, Y., Gerlach, M. H., Trebst, S., and Berg, E. (2016), Phys. Rev. Lett. 117, 097002.Google Scholar
Schmidt, K. E. and Ceperley, D. M. (1992), in The Monte Carlo Method in Condensed Matter Physics, ed. Binder, K. (Springer, Berlin), p. 205.Google Scholar
Schmidt, K. E. and Kalos, M. H. (1984), in Applications of the Monte Carlo Method in Statistical Physics, ed. Binder, K. (Springer, Berlin), p. 125.Google Scholar
Schwenk, A. (2014), Phys. Rev. C 90, 054323.Google Scholar
Shepherd, J. J., Booth, G. H., Grüneis, A., and Alavi, A. (2012), Phys. Rev. B 85, 081103 (R).Google Scholar
Skilling, J. (ed.) (1989), Maximum Entropy and Bayesian Methods (Kluwer, Dordrecht).Google Scholar
Suzuki, M. (1966), J. Phys. Soc. Jpn. 21, 2274.Google Scholar
Suzuki, M. (1971), Prog. Theor. Phys. 46, 1337.Google Scholar
Suzuki, M. (1976a), Commun. Math. Phys. 51, 183.Google Scholar
Suzuki, M. (1976b), Prog. Theor. Phys. 56, 1454.Google Scholar
Suzuki, M. (ed.) (1986), Quantum Monte Carlo Methods (Springer, Berlin).Google Scholar
Suzuki, M. (ed.) (1992), Quantum Monte Carlo Methods in Condensed Matter Physics (World Scientific, Singapore).Google Scholar
Trivedi, N. and Ceperley, D. M. (1989), Phys. Rev. B 40, 2737.Google Scholar
Todo, S., Matsuo, H., and Shitara, H. (2019), Comput. Phys. Commun. 239, 84.Google Scholar
Trotter, H. F. (1959), Proc. Am. Math. Soc. 10, 545.Google Scholar
Troyer, M., Wessel, S., and Alet, F. (2003), Phys. Rev. Lett. 90, 120201.Google Scholar
Troyer, M., and Wiese, U.-J. (2005), Phys. Rev. Lett. 94, 170201.Google Scholar
Wlazłowski, G., Holt, J. W., Moroz, S., Bulgac, A., and Roche, K. J. (2014), Phys. Rev. Lett. 113, 182503.Google Scholar

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  • Quantum Monte Carlo methods
  • David Landau, University of Georgia, Kurt Binder, Johannes Gutenberg Universität Mainz, Germany
  • Book: A Guide to Monte Carlo Simulations in Statistical Physics
  • Online publication: 24 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108780346.009
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  • Quantum Monte Carlo methods
  • David Landau, University of Georgia, Kurt Binder, Johannes Gutenberg Universität Mainz, Germany
  • Book: A Guide to Monte Carlo Simulations in Statistical Physics
  • Online publication: 24 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108780346.009
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  • Quantum Monte Carlo methods
  • David Landau, University of Georgia, Kurt Binder, Johannes Gutenberg Universität Mainz, Germany
  • Book: A Guide to Monte Carlo Simulations in Statistical Physics
  • Online publication: 24 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108780346.009
Available formats
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