Skip to main content
Log in

Enumeration of many-body skeleton diagrams

  • Solid and Condensed State Physics
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for self-energy, polarization, propagator, effective potential, and vertex function, dressed (skeleton) Feynman diagrams are enumerated. Such diagram counts provide useful simple checks for extensions of the theory for future realistic simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002)

    Article  Google Scholar 

  • W.G. Aulbur, L. Jönsson, J.W. Wilkins, Solid State Physics, edited by H. Ehrenreich, F. Spaepen (Academic, New York, 2000), Vol. 54, p. 1

  • F. Aryasetiawan, O. Gunnarsson, Rep. Progr. Phys. 61, 237 (1998)

    Article  ADS  Google Scholar 

  • J.D. Bjorken, S.D. Drell, Relativistic Quantum Fields (McGraw Hill, New York, 1965)

  • A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)

  • L.G. Molinari, Phys. Rev. B 71, 113102 (2005)

    Article  ADS  Google Scholar 

  • M.V. Sadovskii, Soviet Physics JETP 50, 989 (1979)

    Google Scholar 

  • M.V. Sadovskii, A.A. Timofeev, J. Moscow Phys. Soc. 1, 391 (1991)

    Google Scholar 

  • R.H. McKenzie, D. Scarratt, Phys. Rev. B 54, R12709 (1996)

  • J. Schmalian, D. Pines, B. Stojković, Phys. Rev. B 60, 667 (1999)

    Article  ADS  Google Scholar 

  • J. D'Anna, A. Zee, Phys. Rev. E 53, 1399 (1996)

    Article  ADS  Google Scholar 

  • E. Brézin, C. Itzykson, G. Parisi, J.B. Zuber, Comm. Math. Phys. 59, 35 (1978)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • D.V. Boulatov, V.A. Kazakov, Phys. Lett. B 186, 379 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  • P. Zinn-Justin, Some Matrix Integrals related to Knots and Links, in Random Matrix Models and their Applications, MSRI Publications, Vol. 40, edited by P. Bleher, A. Its (Cambridge University Press, 2001) e-print arXiv:math-ph/9910010

  • G. Cicuta, L. Molinari, E. Montaldi, Phys. Lett. B 306, 245 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  • I.M. Suslov, Zh. Eksp. Teor. Fiz. 127, 1350 (2005); I.M. Suslov, Sov. Phys. JETP 100, 1188 (2005) e-print arXiv:hep-th/0510142

    Google Scholar 

  • G. Parisi, Phys. Lett. B 68, 361 (1977)

    Article  ADS  Google Scholar 

  • B. Lautrup, Phys. Lett. B 69, 109 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  • L. Hedin, Phys. Rev. 139, A796 (1965)

  • L. Hedin, S. Lundqvist, Solid State Physics, edited by F. Seitz, D. Turnbull, H. Ehrenreich (Academic, New York, 1969), Vol. 23, p. 1

  • A. Pelster, H. Kleinert, M. Bachmann, Ann. Phys. 297, 363 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • A. Pelster, K. Glaum, Phys. Status Solidi B 237, 72 (2003)

    Article  ADS  Google Scholar 

  • C. Itzykson, J.P. Zuber, Quantum Field Theory (McGraw Hill, New York, 1980)

  • A. Schindlmayr, R.W. Godby, Phys. Rev. Lett. 80, 1702 (1998)

    Article  ADS  Google Scholar 

  • F. Bruneval, F. Sottile, V. Olevano, R. Del Sole, L. Reining, Phys. Rev. Lett. 94, 186402 (2005)

    Article  ADS  Google Scholar 

  • R.J. Riddell, Phys. Rev. 91, 1243 (1953)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • A.G. Basuev, A.N. Vasil'ev, Theor. Math. Phys. 18, 129 (1974)

    Article  MathSciNet  Google Scholar 

  • P. Cvitanovic, B. Lautrup, R.B. Pearson, Phys. Rev. D 18, 1939 (1978)

    Article  ADS  Google Scholar 

  • E.N. Argyres, A.F.W. van Hameren, R.H.P. Kleiss, C.G. Papadopoulos, Eur. Phys. J. C 19, 567 (2001)

    MATH  MathSciNet  ADS  Google Scholar 

  • R.J. Mathar, e-print arXiv:physics/0512022

  • É.Z. Kuchinskii, M.V. Sadovskii, J. Exp. Theor. Phys. 86, 367 (1998)

    Article  Google Scholar 

  • I.M. Suslov, Sov. Phys. JETP 75, 1049 (1992)

    Google Scholar 

  • C.-O. Almbladh, U. Von Barth, R. Van Leeuwen, Int. J. Mod. Phys. B 13, 535 (1999)

    Article  ADS  Google Scholar 

  • G.F. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, 2005)

  • K. Kajantie, M. Laine, Y. Schröder, Phys. Rev. D 65, 045008 (2002)

    Article  ADS  Google Scholar 

  • C. Itzykson, G. Parisi, J.B. Zuber, Phys. Rev. D 16, 996 (1977)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Manini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molinari, L., Manini, N. Enumeration of many-body skeleton diagrams. Eur. Phys. J. B 51, 331–336 (2006). https://doi.org/10.1140/epjb/e2006-00223-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2006-00223-9

PACS.

Navigation