Abstract
Since Metropolis’s work, the Monte Carlo method has been applied not only to various statistical problems of classical systems, but also to many quantum mechanical systems. In this chapter, we briefly describe the extension of the Monte Carlo method to quantum mechanical systems.
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References
D. M. Ceperley and M. H. Kalos, in Monte Carlo Methods in Statistical Physics, edited by K. Binder (Springer, Berlin, Heidelberg, 1979) Chapter 4.
K. E. Schmidt and D. M. Ceperley, in The Monte Carlo Method in Condensed Matter Physics, edited by K. Binder, 2nd ed. (Springer, Berlin, Heidelberg, 1995) Chapter 7.
A. Bijl, Physica 7, 869 (1940).
R. B. Dingle, Philos. Mag. 40, 573 (1949); R. Jastrow, Phys. Rev. 98, 1479 (1955); N. F. Mott, Philos. Mag. 40, 61 (1949).
C. W. Greeff, W. A. Lester and B. L. Hammond, in Recent Advances in Quantum Monte Carlo Methods, edited by W. A. Lester, Jr. (World Scientific, Singapore, 1997) p. 117.
G. E. Forsythe and R. A. Leibler, MTAC 4, 127 (1950).
J. Kuti and J. Polonyi, Proc. XXI International Conference on High Energy Physics, Paris (1982).
C. W. Greeff, W. A. Lester and B. L. Hammond, J. Chem. Phys. 104, 1973 (1996).
B. L. Hammond, W. A. Lester and P. J. Reynolds, Monte Carlo Methods in ab-initio Quantum Chemistry (World Scientific, Singapore, 1994).
J. C. Grossman, L. Mitas and K. Raghavachari, Phys. Rev. Lett. 75, 3870 (1995); W. A. Lester, in Recent Advances in Quantum Monte Carlo Methods, edited by W. A. Lester, Jr. (World Scientific, Singapore, 1997), p. 133.
G. Rajagopal, R. J. Needs, S. Kenny, W. M. C. Foulkes and A. James, Phys. Rev. Lett. 73, 1959 (1994).
A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, Boston, MA, 1971).
J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Redwood City, CA, 1988).
H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959).
M. Takahashi and M. Imada, J. Phys. Soc. Jpn. 53, 963,3765,3770 (1984); F. F. Abraham, Computer Simulation Studies in Condensed-Matter Physics, edited by D. P. Landau, K. K. Mon and H.-B. Schüttler (Springer, Berlin, Heidelberg, 1988) p. 134.
J. Hirsch, D. J. Scalapino, R.L.Sugar, and R. Blankenbecker, Phys. Rev. Lett. 47, 1628 (1981); Phys. Rev. 26, 5033 (1982).
R. P. Feynman, Statistical Mechanics (W. A. Benjamin, New York, 1972).
M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976); M. Suzuki, S. Miyashita, and A. Kuroda, Prog. Theor. Phys. 58, 1377 (1977).
M. Suzuki in Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, Solid-State Sciences, Vol. 74 (Springer, Berlin, Heidelberg, 1987).
Y. Okabe and M. Kikuchi, Phys. Rev. B 34, 7896 (1986).
Y. Okabe and M. Kikuchi, J. Phys. Soc. Jpn. 56, 1963 (1987).
Y. Okabe and M. Kikuchi, J. Phys. Soc. Jpn. 57, 4351 (1988).
G. Parisi and Y. Wu, Sci. Sin. 24, 483 (1981).
J. E. Hirsch, Phys. Rev. Lett. 51, 1960 (1983); Phys. Rev. B 31, 4403 (1985).
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© 1999 Springer-Verlag Berlin Heidelberg
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Ohno, K., Esfarjani, K., Kawazoe, Y. (1999). Quantum Monte Carlo (QMC) Methods. In: Computational Materials Science. Springer Series in Solid-State Sciences, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59859-3_6
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DOI: https://doi.org/10.1007/978-3-642-59859-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64155-8
Online ISBN: 978-3-642-59859-3
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