Real-Space Renormalization-Group Method for Quantum Systems: Application to Quantum Frustration in Two Dimensions

  • K. A. Penson
  • R. Jullien
  • P. Pfeuty
  • K. Uzelac
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 9)

Abstract

A real-space renormalization-group method well suited for studying phase transitions at T = 0 in quantum systems is presented and applied to a generalized spin 1/2 planar hamiltonian on the triangular lattice, which includes ferromagnetic and anti-ferromagnetic XY models as limiting cases. This provides a description of the effects of frustration in quantum systems.

Keywords

Tral Nite Ferro Weinstein 

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References

  1. 1a.
    M. Suzuki, Prog. Theor. Phys. 46, 1337 (1971);CrossRefMATHADSGoogle Scholar
  2. 1b.
    M. Suzuki, Prog. Theor. Phys. 56,1454 (1976)CrossRefMATHADSGoogle Scholar
  3. 2.
    C. J. Thompson, in “Phase transitions and critical phenomena”, vol. I, C. Domb and M. S. Green ed. Academic Press, 1972Google Scholar
  4. 3a.
    S. D. Drell, M. Weinstein and S. Yankielovicz, Phys. Rev. D 14 487 (1976);CrossRefADSGoogle Scholar
  5. 3b.
    S. D. Drell, M. Weinstein and S. Yankielovicz, Phys. Rev. D 14, 1628 (1976);ADSGoogle Scholar
  6. 3c.
    S. D. Drell, M. Weinstein and S. Yankielovicz, Phys. Rev. D 16, 1769 (1977) S. D. Drell;CrossRefADSGoogle Scholar
  7. 3d.
    M. Svetitsky and M. Weinstein, Phys. Rev. D 17, 523 (1978)CrossRefADSMathSciNetGoogle Scholar
  8. 3e.
    S. D. Drell and M. Weinstein, Phys. Rev. D 17, 3203 (1978)CrossRefADSMathSciNetGoogle Scholar
  9. 4.
    K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975)CrossRefADSGoogle Scholar
  10. 5a.
    R. Jullien, J. N. Fields and S. Doniach, Phys. Rev. Lett. 38, 1500 (1977);CrossRefADSGoogle Scholar
  11. 5b.
    R. Jullien, J. N. Fields and S. Doniach, Phys. Rev. B 16, 4889 (1977)CrossRefADSGoogle Scholar
  12. 6.
    R. Jullien, P. Pfeuty, J. N. Fields and S. Doniach, Phys. Rev. B 18, 3568 (1978)CrossRefADSGoogle Scholar
  13. 7.
    K. A. Penson, R. Jullien and P. Pfeuty, Phys. Rev. B 19, 4653 (1979)CrossRefADSGoogle Scholar
  14. 8.
    K. A. Penson, R. Jullien and P. Pfeuty, J. Phys. C 12, 3967 (1979)CrossRefADSGoogle Scholar
  15. 9.
    R. Jullien, K. A. Penson and P. Pfeuty, J. Physique (France) 40, L 237 (1979)CrossRefGoogle Scholar
  16. 10.
    R. Jullien and P. Pfeuty, Phys. Rev. B 19, 4646 (1979)CrossRefADSGoogle Scholar
  17. 11.
    K. A. Penson, R. Jullien and P. Pfeuty, Phys. Rev. B (1980)Google Scholar
  18. 12.
    K. Uzelac, K. A. Penson, R. Jullien and P. Pfeuty, J. Phys. A 12, L 295 (1979)CrossRefADSGoogle Scholar
  19. 13.
    K. Uzelac, P. Pfeuty and R. Jullien, Phys. Rev. Lett. 43, 805 (1979), K. Uzelac, R. Jullien and P. Pfeuty, Phys. Rev. B (1980) K. Uzelac, R. Jullien, P. Moussa and P. Pfeuty, this conferenceCrossRefADSGoogle Scholar
  20. 14.
    R. Jullien, P. Pfeuty, A. K. Bhattacharjee and B. Coqblin, J. of Applied Phys. 50, 7555 (1979)CrossRefADSGoogle Scholar
  21. 15.
    P. Pfeuty, R. Jullien and K. A. Penson, in preparationGoogle Scholar
  22. 16.
    R. Jullien, K. A. Penson, P. Pfeuty and K. Uzelac, Phys. Rev. Lett, to be published.Google Scholar
  23. 17.
    L. G. Marland and D. D. Betts, Phys. Rev. Lett. 43, 1618 (1979)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • K. A. Penson
    • 1
  • R. Jullien
    • 1
  • P. Pfeuty
    • 1
  • K. Uzelac
    • 1
  1. 1.Laboratoire de Physique des SolidesUniversité Paris Sud Centre d’OrsayOrsay CédexFrance

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