Correlated Wavefunction Quantum Monte-Carlo Approach to Solids

  • S. G. Louie
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 114)

Abstract

A method for calculating the electronic and structural properties of solids using correlated wavefunctions together with quantum Monte Carlo techniques is described. The approach retains the exact Coulomb interaction between the electrons and employs a many-electron wavefunction of the Jastrow-Slater form. Several examples are given to illustrate the utility of the method. Topics discussed include the cohesive properties of bulk semiconductors, the magnetic-field-induced Wigner crystal in two dimensions, and the magnetic structure of bcc hydrogen. Landau level mixing is shown to be important in determining the transition between the fractional quantum Hall liquid and the Wigner crystal. Information on electron correlations such as the pair correlation functions which are not accessible to one-electron theories is also obtained.

Keywords

Crystallization Graphite GaAs Lime Expense 

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References

  1. 1.
    S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. Lett. 61, 1631 (1988); Phys. Rev.B. 42, 3503 (1990); 43, 9299 (E) (1991).CrossRefGoogle Scholar
  2. 2.
    B. Kiel, G. Stollhoff, C. Weigel, P. Fulde, and H. Stoll, Z Phys. B 46, 1 (1982); G. Stollhoff and K. P. Bohnen, Phys. Rev. B 37, 4678 (1988).CrossRefGoogle Scholar
  3. 3.
    X. P. Li, D. M. Ceperley, and R. M. Martin, Phys. Rev. B 44, 10929 (1991).CrossRefGoogle Scholar
  4. 4.
    E. Y. Andred et al., Phys. Rev. Lett. 60, 2765 (1988); H. W. Jiang et al., ibid. 65, 633 (1990); V. J. Goldman et al., ibid. 65, 2189 (1990); Buhmann et al., ibid. 66, 926 (1991); H. W. Jiang et al., Phys. Rev. B 44, 8107 (1991).CrossRefGoogle Scholar
  5. 5.
    M. B. Santos et al., Phys. Rev. Lett 68, 1188 (1992).CrossRefGoogle Scholar
  6. 6.
    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).CrossRefGoogle Scholar
  7. 7.
    S. Fahy. X.-W. Wang, and S. G. Louie, Phys. Rev. Lett. 65, 1478 (1990).CrossRefGoogle Scholar
  8. 8.
    X. W. Wang, J. Zhu, S. G. Louie, and S. Fahy, Phys. Rev. Lett. 65, 2414 (1990).CrossRefGoogle Scholar
  9. 9.
    X. J. Zhu and S. G. Louie, to be published.Google Scholar
  10. 10.
    There is a large scatter in the experimentally measured cohesive energy of Si. See, for example, Ref. 1 and references therein.Google Scholar
  11. 11.
    R. P. Feynmann, Phys. Rev. 94, 262 (1954).CrossRefGoogle Scholar
  12. 12.
    Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, ed. O. Madelung (Springer-Verlag, New York, 1982), Vol. 17.Google Scholar
  13. 13.
    M. S. Hybertsen and S. G. Louie, Phys. Rev. B 32, 7005 (1985); S. Horsch, P. Horscn, and P. Fulde, ibid. 1870 (1984);Google Scholar
  14. 14.
    The Quantum Hall Effect, eds. R. E. Prange and S. M. Girvin (Springer-Verlag, New York, 1990), 2nd ed.Google Scholar
  15. 15.
    D. Yoshioka and H. Fukuyama, J. Phys. Soc. Jap. 47, 394 (1979); D. Yoshioka and P. A. Lee, Phys. Rev. B 27, 4986 (1983); K. Maki and X. Zotos, Phys. Rev. B 28, 4349 (1983).CrossRefGoogle Scholar
  16. 16.
    P. K. Lam and S. M. Girvin, Phys. Rev. B 30, 473 (1984); 31, 613 (E) (1985).CrossRefGoogle Scholar
  17. 17.
    R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983); D. Levesque, J. J. Weis, and A. H. MacDonald, Phys. Rev. B 30, 1056 (1984).CrossRefGoogle Scholar
  18. 18.
    A. H. MacDonald, Phys. Rev. B 30, 4392 (1984); D. Yoshioka, J. Phys. Soc. Jpn. 53, 3740 (1984); 55, 885 (1986); K. Esfarjani and S. T. Chui, J. Phys. C 3, 5825 (1991)CrossRefGoogle Scholar
  19. 19.
    See, for example, J. Callaway, Quantum Theory of the Solid State (Academic Press, New York, 1974).Google Scholar
  20. 20.
    H. L. Stormer et al., Phys. Rev. Lett 51, 126 (1983).CrossRefGoogle Scholar
  21. 21.
    R. Price, P. M. Platzman, and S. He, to be published.Google Scholar
  22. 22.
    J. Zhu, X. W. Wang, and S. G. Louie, to be published.Google Scholar
  23. 23.
    B. I. Min, T. Oguchi, H. J. F. Jansen, and A. J. Freeman, Phys. Rev. B 33, 324 (1986).CrossRefGoogle Scholar
  24. 24.
    A. Svane and O. Günnarson, Solid State Comm. 76, 851 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • S. G. Louie
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of California at BerkeleyBerkeleyUSA
  2. 2.Materials Sciences DivisionLawrence Berkeley LaboratoryBerkeleyUSA

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