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Conserving Approximations vs. Two-Particle Self-Consistent Approach

  • S. Allen
  • A. -M. S. Tremblay
  • Y. M. Vilk
Chapter
  • 910 Downloads
Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

The conserving approximation scheme to many-body problems was developed by Kadanoff and Baym using the functional-derivative approach. Another approach for the Hubbard model also satisfies conservation laws, but in addition it satisfies the Pauli principle and a number of sum rules. A concise formal derivation of that approach, using functional derivatives, is given in this conference paper to highlight formal analogies and differences with conserving approximations.

Keywords

Hubbard Model Random Phase Approximation Functional Derivative Pauli Principle Quantum Monte Carlo 
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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5 References

  1. [1]
    G. Baym, Phys. Rev. 127 (1962), 1391.CrossRefADSzbMATHMathSciNetGoogle Scholar
  2. [2]
    L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin, Menlo Park, 1962.zbMATHGoogle Scholar
  3. [3]
    N.E. Bickers and D.J. Scalapino, Ann. Physics 193 (1989), 206.CrossRefADSGoogle Scholar
  4. [4]
    Y.M. Vilk and A.-M.S. Tremblay, J. Physique I France 7 (1997), 1309.CrossRefADSGoogle Scholar
  5. [5]
    Y.M. Vilk and A.-M.S. Tremblay, Europhys. Lett. 33 (1996), 159; J. Phys. Chem. Solids 56 (1995), 1769.CrossRefADSGoogle Scholar
  6. [6]
    P.C.E. Stamp, J. Phys. F: Met. Phys. 15 (1985), 1829.CrossRefADSGoogle Scholar
  7. [7]
    S. Allen and A.-M.S. Tremblay, Phys. Rev. B 64 (2001), 075115/1–14.CrossRefADSGoogle Scholar
  8. [8]
    B. Kyung, S. Allen, and A.-M.S. Tremblay, Phys. Rev. B 64 (2001),075116.CrossRefADSGoogle Scholar
  9. [9]
    P.C. Martin and J. Schwinger, Phys. Rev. 115 (1959). This paper also contains numerous references to previous work.Google Scholar
  10. [10]
    For a review, see K.S. Singwi and M.P. Tosi, in eds. H. Ehrenreich, F. Seitz, and D. Turnbull, Solid State Physics, Vol. 36 (Academic, New York, 1981), p. 177; S. Ichimaru, Rev. Modern Phys. 54 (1982), 1017.Google Scholar
  11. [11]
    Y.M. Vilk, L. Chen, and A.-M.S. Tremblay, Phys. Rev. B Rapid Comm. 49 (1994), 13267.ADSGoogle Scholar
  12. [12]
    B. Kyung, J.-S. Landry, D. Poulin, and A.-M.S. Tremblay, Phys. Rev. Lett. 90 (2003), 099702.CrossRefADSGoogle Scholar
  13. [13]
    A.F. Veilleux, A.-M. Daré, L. Chen, Y.M. Vilk, and A.-M.S. Tremblay, Phys. Rev. B 52 (1995), 16255.CrossRefADSGoogle Scholar
  14. [14]
    A.-M. Daré, Y.M. Vilk, and A.-M.S. Tremblay, Phys. Rev. B 53(1996), 14236.CrossRefADSGoogle Scholar
  15. [15]
    N. Bulut, D.J. Scalapino, and S.R. White, Phys. Rev. B 47 (1993), 2742; N.F. Berk and J.R. Schrieffer, Phys. Rev. Lett. 17 (1966), 433.CrossRefADSGoogle Scholar
  16. [16]
    S. Allen, H. Touchette, S. Moukouri, Y.M. Vilk, and A.-M.S. Tremblay, Phys. Rev. Lett. 83 (1999), 4128; Y.M. Vilk, S. Allen, H. Touchette, S. Moukouri, L. Chen, and A.-M.S. Tremblay, J. Phys. Chem. Solids 59 (1998), 1873.CrossRefADSGoogle Scholar
  17. [17]
    S. Moukouri, S. Allen, F. Lemay, B. Kyung, D. Poulin, Y.M. Vilk, and A.-M. S. Tremblay, Phys. Rev. B 61 (2000), 7887.CrossRefADSGoogle Scholar
  18. [18]
    S. Allen, Ph.D. Thesis, Université de Sherbrooke, 2000 (unpublished).Google Scholar
  19. [19]
    S. Roy, M.Sc. thesis, Université de Sherbrooke, 2002 (unpublished).Google Scholar
  20. [20]
    A.-M. Daré (unpublished).Google Scholar
  21. [21]
    S. Allen, B. Kyung, and A.-M.S. Tremblay (unpublished).Google Scholar
  22. [22]
    B. Kyung, J.-S. Landry, and A.-M.S. Tremblay, cond-mat/0205165.Google Scholar
  23. [23]
    B. Kyung, Phys. Rev. B 63 (2000), 014502; Phys. Rev. B 64 (2001), 104512.CrossRefADSGoogle Scholar
  24. [24]
    S. Allen (unpublished).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2004

Authors and Affiliations

  • S. Allen
  • A. -M. S. Tremblay
  • Y. M. Vilk

There are no affiliations available

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