Journal of Statistical Physics

, Volume 82, Issue 1–2, pp 131–153 | Cite as

Cluster algorithms for anisotropic quantum spin models

  • Naoki Kawashima


We present cluster Monte Carlo algorithms for theXYZ quantum spin models. In the special case ofS=1/2, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study theS=1/2XY model in two dimensions with a representation in which the quantization axis lies in the easy plane. We find that the numerical autocorrelation time for the cluster algorithm remains of the order of unity and does not show any significant dependence on the temperature, the system size, or the Trotter number. On the other hand, the autocorrelation time for the conventional algorithm strongly depends on these parameters and can be very large. The use of improved estimators for thermodynamic averages further enhances the efficiency of the new algorithms.

Key Words

Quantum Monte Carlo cluster algorithm XYZ model Heisenberg model XY model 


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  1. 1.
    P. W. Kasteleyn and F. M. Fortuin,J. Phys. Soc. Jpn. 26 (Suppl.):11 (1969); C. M. Fortuin and P. W. Kasteleyn,Physica 57:536 (1972).Google Scholar
  2. 2.
    R. H. Swendsen and J.-S. Wang,Phys. Rev. Lett. 58:86 (1987).CrossRefPubMedGoogle Scholar
  3. 3.
    N. Kawashima and J. E. Gubernatis,J. Stat. Phys. 80:169 (1995).CrossRefGoogle Scholar
  4. 4.
    N. Kawashima and J. E. Gubernatis,Phys. Rev. Lett. 73:1295 (1994).CrossRefGoogle Scholar
  5. 5.
    H. G. Evertz, M. Marcu, and G. Lana,Phys. Rev. Lett. 70:875 (1993); H. G. Evertz and M. Marcu, inQuantum Monte Carlo Method in Condensed Matter Physics, M. Suzuki, ed. (World Scientific, Singapore, 1992), p. 65.CrossRefGoogle Scholar
  6. 6.
    N. Kawashima, J. E. Gubernatis, and H. G. Evertz,Phys. Rev. B. 50:136 (1994).CrossRefGoogle Scholar
  7. 7.
    M. Suzuki,Prog. Theor. Phys. 56:1454 (1976).Google Scholar
  8. 8.
    M. Jarrell and J. E. Gubernatis, In preparation.Google Scholar
  9. 9.
    H.-Q. Ding and M. S. Makivić,Phys. Rev. B 42:6827 (1990).CrossRefGoogle Scholar
  10. 10.
    H.-Q. Ding,Phys. Rev. B 45:230 (1992).CrossRefGoogle Scholar
  11. 11.
    M. P. Allen and D. J. Tildesley,Computer Simulations of Liquids (Oxford University Press, Oxford, 1987), Chapter 6.Google Scholar
  12. 12.
    M. S. Makivić and H.-Q. Ding,Phys. Rev. B 43:3562 (1991).CrossRefGoogle Scholar
  13. 13.
    U. Wolff,Phys. Rev. Lett. 60:1461 (1988); U. Wolff,Nucl. Phys. 300[FS22]:501 (1988).CrossRefPubMedGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Naoki Kawashima
    • 1
    • 2
  1. 1.Los Alamos National LaboratoryCenter for Nonlinear Studies and Theoretical DivisionLos Alamos
  2. 2.Department of PhysicsUniversity of TokyoBunkyo, TokyoJapan

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