High-Speed Algorithm for Quantum Monte Carlo Simulation

  • Y. Okabe
  • M. Kikuchi
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 74)


This paper is concerned with a high-speed algorithm for Monte Carlo simulation of the quantum spin system using the Suzuki-Trotter formula. We introduce a binary-number spin representation using logical commands. The calculation is fully vectorized by decomposing into appropriate sublattices. The one-dimensional antiferromagnetic Heisenberg model (S=1/2) is studied for the Trotter number m≤32 to check the efficiency of our algorithm. We deal with both the pair-spin decomposition and the cluster-spin decomposition approximations.


Monte Carlo Simulation Ising Model Global Process Heisenberg Model Monte Carlo Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Wansleben, J.G. Zabolitsky and C. Kalle: J. Stat. Phys. 37, 271 (1984);ADSCrossRefGoogle Scholar
  2. C. Kalle: J. Phys. A17, L801 (1984)ADSGoogle Scholar
  3. 2.
    M. Kikuchi and Y. Okabe: Prog. Theor. Phys. 74, 458 (1985);ADSCrossRefGoogle Scholar
  4. M. Kikuchi and Y. Okabe: J. Phys. Soc. Jpn. 55, 1359 (1986)ADSCrossRefGoogle Scholar
  5. 3.
    S. Wansleben: to be publishedGoogle Scholar
  6. 4.
    G.O. Williams and M.H. Kalos: J. Stat. Phys. 37, 283 (1984)ADSCrossRefGoogle Scholar
  7. 5.
    G. Bhanot, D. Duke and R. Salvador: Phys. Rev. B33, 7841 (1986)ADSCrossRefGoogle Scholar
  8. 6.
    M. Kikuchi and Y. Okabe: to be publishedGoogle Scholar
  9. 7.
    M. Suzuki: Prog. Theor. Phys. 56, 1454 (1976)ADSMATHCrossRefGoogle Scholar
  10. 8.
    H. De Raedt and A. Lagendijk: Phys. Rep. 127, 233 (1985)MathSciNetADSCrossRefGoogle Scholar
  11. 9.
    M. Suzuki: J. Stat. Phys. 43, 883 (1986)ADSCrossRefGoogle Scholar
  12. 10.
    M. Suzuki, S. Miyashita and A. Kuroda: Prog. Theor. Phys. 58, 1377 (1977)ADSMATHCrossRefGoogle Scholar
  13. 11.
    J.E. Hirsch, R.L. Sugar, D.J. Scalapino and R. Blankenbecler: Phys. Rev. B26, 5033 (1982)ADSCrossRefGoogle Scholar
  14. 12.
    J.L. Cullen and D.P. Landau: Phys. Rev. B27, 297 (1983)ADSCrossRefGoogle Scholar
  15. 13.
    T. Sakaguchi, K. Kubo and S. Takada: J. Phys. Soc. Jpn. 54, 861 (1985)ADSCrossRefGoogle Scholar
  16. 14.
    M. Marcu and A. Wiesler: J. Phys. A18, 2479 (1985);ADSGoogle Scholar
  17. M. Marcu, J. Muller and F.K. Schmatzer: J. Phys. A18, 3189 (1985)ADSGoogle Scholar
  18. 15.
    Y. Okabe and M. Kikuchi: Phys. Rev. B34, No. 11 (1986)Google Scholar
  19. 16.
    H. Betsuyaku: Phys. Rev. Lett. 53, 629 (1984);MathSciNetADSCrossRefGoogle Scholar
  20. H. Betsuyaku: Prog. Theor. Phys. 73, 319 (1985)ADSCrossRefGoogle Scholar
  21. 17.
    T. Tsuzuki: Prog. Theor. Phys. 73, 1352 (1985);MathSciNetADSMATHCrossRefGoogle Scholar
  22. T. Tsuzuki: Prog. Theor. Phys. 75, 225 (1986)MathSciNetADSCrossRefGoogle Scholar
  23. 18.
    T. Yokota and H. Betsuyaku: Prog. Theor. Phys. 75, 46 (1986)ADSCrossRefGoogle Scholar
  24. 19.
    H. Betsuyaku: Prog. Theor. Phys. 75, 774 (1986)ADSCrossRefGoogle Scholar
  25. 20.
    H. Betsuyaku and T. Yokota: Prog. Theor. Phys. 75, 808 (1986)ADSCrossRefGoogle Scholar
  26. 21.
    S. Katsura: Phys. Rev. 127, B1508 (1962)ADSCrossRefGoogle Scholar
  27. 22.
    M. Barma and B.S. Shastry: Phys. Rev. B18, 3351 (1978)ADSCrossRefGoogle Scholar
  28. 23.
    A. Wiesler: Phys. Lett. 89A, 359 (1982)CrossRefGoogle Scholar
  29. 24.
    Instead of using the term, the ‘local’ process, as in Ref. 15, we here use the ‘loop’ process for the consistency with the case of the cluster-spin decompositionGoogle Scholar
  30. 25.
    J.C. Bonner and M.E. Fisher: Phys. Rev. 135, A640 (1964)ADSCrossRefGoogle Scholar
  31. 26.
    M. Suzuki: Phys. Rev. B31, 2957 (1985);ADSGoogle Scholar
  32. M. Suzuki: J. Math. Phys. 26, 601 (1985);MathSciNetADSMATHCrossRefGoogle Scholar
  33. M. Suzuki: Phys. Lett. 113A, 289 (1985)CrossRefGoogle Scholar
  34. 27.
    R.B. Griffiths: Phys. Rev. 133, A768 (1964)ADSCrossRefGoogle Scholar
  35. 28.
    T. Tsuzuki: private communicationGoogle Scholar
  36. 29.
    M. Takahashi and M. Yamada: J. Phys. Soc. J.n. 54, 2808 (1985);ADSCrossRefGoogle Scholar
  37. M. Yamada and M. Takahashi: J. Phys. Soc. Jpn. 55, 2024 (1986)ADSCrossRefGoogle Scholar
  38. 30.
    T. Kimura, I. Harada and T. Tonegawa: private communicationGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Y. Okabe
    • 1
  • M. Kikuchi
    • 1
  1. 1.Department of PhysicsTohoku UniversitySendai 980Japan

Personalised recommendations