Decoupled Cell Monte Carlo Method for Quantum Spin Systems

  • S. Homma
  • K. Sano
  • H. Matsuda
  • N. Ogita
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 74)

Abstract

A decoupled cell method is proposed as a new method of Monte Carlo simulation for quantum spin systems. Thermodynamic quantities such as internal energy, in-plane and out-of-plane susceptibilities and spin pair correlation functions are calculated by this method in the 1D XY model. The results obtained agree well with the exact ones except for very low temperatures, indicating the validity of this method. Further application of this method strongly suggests (1) the existence of a phase transition in the quantum XY model on the square lattice similar to the Kosterlitz-Thouless transition in the classical XY model, and (2) the existence of a sublattice structure composed of three lattices which is short-ranged both spatially and temporally in the antiferromagnetic Heisenberg model on the triangular lattice.

Keywords

High Temperature Phase Triangular Lattice Monte Carlo Calculation Monte Carlo Step Spin Configuration 
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.
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References

  1. 1.
    D. C. Handscomb, Proc.Cambridge Philos. Soc., 58 (1962), 594MathSciNetADSMATHCrossRefGoogle Scholar
  2. D. C. Handscomb, Proc.Cambridge Philos. Soc., 60 (1964), 115MathSciNetADSCrossRefGoogle Scholar
  3. 2.
    M. Suzuki, Prog. Theor. Phys. 56 (1976), 1454ADSMATHCrossRefGoogle Scholar
  4. 3.
    M. Suzuki, Phys. Rev. B31 (1985), 2957ADSGoogle Scholar
  5. M. Suzuki, J. Stat. Phys. 43 (1986), 883ADSCrossRefGoogle Scholar
  6. 4.
    S. Chakravarty and D. B. Stein, Phys. Rev. Lett., 49 (1982), 582ADSCrossRefGoogle Scholar
  7. 5.
    J. W. Lyklema, Phys. Rev. Lett., 49 (1982), 88ADSCrossRefGoogle Scholar
  8. J. W. Lyklema, Phys. Rev. B27 (1983), 3108ADSCrossRefGoogle Scholar
  9. 6.
    D. H. Lee, J. D. Joannopoulos and J. W. Negele, Phys. Rev. B30 (1984), 1599ADSGoogle Scholar
  10. 7.
    S. Kadowaki and A. Ueda, Prog. Theor. Phys. 75 (1986), 451ADSCrossRefGoogle Scholar
  11. 8.
    M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys. 58 (1977), 1377ADSMATHCrossRefGoogle Scholar
  12. 9.
    J. J. Cullen and D. P. Landau, Phys. Rev. B27 (1983), 297ADSCrossRefGoogle Scholar
  13. 10.
    H. Betsuyaku, Phys. Rev. Lett. 53 (1984), 629MathSciNetADSCrossRefGoogle Scholar
  14. H. Betsuyaku, Prog. Theor. Phys. 73 (1985), 319ADSCrossRefGoogle Scholar
  15. 11.
    T. Yokota and H. Betsuyaku, Prog. Theor. Phys. 75 (1986), 46ADSCrossRefGoogle Scholar
  16. 12.
    H. Takano, Prog. Theor. Phys. 73 (1985), 332ADSCrossRefGoogle Scholar
  17. 13.
    T. Sakaguchi, K. Kubo and S. Takada, J. Phys. Soc. Jpn. 54 (1985), 861ADSCrossRefGoogle Scholar
  18. 14.
    I. Satija, G. Wysin and A. R. Bishop, Phys. Rev. B31 (1985), 3205ADSCrossRefGoogle Scholar
  19. 15.
    E. Loh, Jr., D. J. Scalapino and P. M. Grant, Phys. Rev. B31 (1985), 4712ADSCrossRefGoogle Scholar
  20. 16.
    H. De Raedt, B. De Raedt and A. Lagendijk, Z. Phys. B57 (1984), 209MathSciNetCrossRefGoogle Scholar
  21. 17.
    H. De Raedt and A. Lagendijk, Phys. Rep. 127 (1985), 233MathSciNetADSCrossRefGoogle Scholar
  22. 18.
    M. Takasu, S. Miyashita and S. Suzuki, Prog. Theor. Phys. 75 (1986), 1254ADSCrossRefGoogle Scholar
  23. 19.
    S. Homma, H. Matsuda and N. Ogita, Prog. Theor. Phys. 72 (1984), 1245ADSCrossRefGoogle Scholar
  24. 20.
    S. Homma, H. Matsuda and N. Ogita, Prog. Theor. Phys. 75 (1986), 1068ADSCrossRefGoogle Scholar
  25. 21.
    S. Homma. K. Sano, H. Matsuda and N. Ogita, Prog. Theor. Phys. Suppl. 87Google Scholar
  26. 22.
    S. Katsura, Phys. Rev. 127 (1962), 1508ADSMATHCrossRefGoogle Scholar
  27. 23.
    B. M. McCoy, Phys. Rev. 173 (1968), 531MathSciNetADSCrossRefGoogle Scholar
  28. 24.
    J. M. Kosterlitz and D. J. Thouless, J. Phys. C6 (1973), 1181ADSGoogle Scholar
  29. J. M. Kosterlitz, J. Phys. C7 (1974), 1046ADSGoogle Scholar
  30. 25.
    S. Miyashita, H. Nishimori, A. Kuroda and S. Suzuki, Prog. Theor. Phys. 60 (1978), 1669ADSCrossRefGoogle Scholar
  31. 26.
    J. Tobochinik and G. V. Chester, Phys. Rev. B20 (1979), 3761ADSCrossRefGoogle Scholar
  32. 27.
    J. E. Van Himbergen and S. Chakravarty, Phys. Rev. B23 (1981), 359CrossRefGoogle Scholar
  33. 28.
    K. Y. Szeto and G. Dresselhaus, Phys. Rev. B32 (1984), 3142Google Scholar
  34. 29.
    J. F. Fernandez, M. F. Ferreira and J. Stankiewicz, Phys. Rev. B34 (1986), 292ADSCrossRefGoogle Scholar
  35. 30.
    G. H. Wannier, Phys. Rev. 79 (1950), 357MathSciNetADSMATHCrossRefGoogle Scholar
  36. 31.
    S. Miyashita, J. Phys. Soc. Jpn. 53 (1984), 44ADSCrossRefGoogle Scholar
  37. 32.
    H. Nishimori and S.’ J. Miyake, Prog. Theor. Phys. 73 (1983), 18ADSCrossRefGoogle Scholar
  38. 33.
    S. J. Miyake, Prog. Theor. Phys. 74 (1984), 468ADSCrossRefGoogle Scholar
  39. 34.
    T. Oguchi, H. Nishimori and Y. Taguchi, J. Phys. Soc. Jpn. 55 (1986), 323ADSCrossRefGoogle Scholar
  40. 35.
    S. Miyashita and H. Shiba, J. Phys. Soc. Jpn. 53 (1984), 1145ADSCrossRefGoogle Scholar
  41. 36.
    H. Kawamura and S. Miyashita, J. Phys. Soc. Jpn. 53 (1984), 9, 4138ADSCrossRefGoogle Scholar
  42. 37.
    K. Hirakawa, H. Kadowaki and K. Ubukoshi, J. Phys. Soc. Jpn. 54 (1985), 3526ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • S. Homma
    • 1
  • K. Sano
    • 2
  • H. Matsuda
    • 3
  • N. Ogita
    • 4
  1. 1.Department of Applied PhysicsNagoya UniversityNagoya 464Japan
  2. 2.Department of PhysicsNagoya UniversityNagoya 464Japan
  3. 3.Department of BiologyKyushu UniversityFukuoka 812Japan
  4. 4.The Institute of Physical and Chemical ResearchWakoJapan

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