Strong-Coupling Diagram Technique for Strong Electron Correlations

  • A. ShermanEmail author
Conference paper
Part of the NATO Science for Peace and Security Series A: Chemistry and Biology book series (NAPSA)


Using the strong coupling diagram technique a closed set of equations was derived for the electron Green’s function of the Hubbard model. Spectral functions calculated self-consistently in the two-dimensional t-U model are in qualitative and in some cases quantitative agreement with results of Monte Carlo simulations in a wide range of electron concentrations. For three different initial bands – the semi-elliptical density of states, t-U and t-t′-U models – the Mott transition occurs at very close values of the Hubbard repulsion \(U_{c} \approx \sqrt{3}\varDelta /2\), where Δ is the initial bandwidth. The behavior of the Mott gap with doping and its width at half-filling depend strongly on the value of the next-nearest hopping constant t′.



This work was supported by the research project IUT2-27, the European Regional Development Fund TK114 and the Estonian Scientific Foundation (grant ETF-9371).


  1. 1.
    Vladimir MI, Moskalenko VA (1990) Theor Math Phys 82:301CrossRefGoogle Scholar
  2. 2.
    Metzner W (1991) Phys Rev B 43:8549ADSCrossRefGoogle Scholar
  3. 3.
    Sherman A (2006) Phys Rev B 73:155105; 74:035104 (2006)Google Scholar
  4. 4.
    Sherman A (2015) Physica B 456:35ADSCrossRefGoogle Scholar
  5. 5.
    Hubbard J (1964) Proc R Soc Lond A 281:401ADSCrossRefGoogle Scholar
  6. 6.
    Sherman A (2015) Int J Mod Phys B 29:1550088ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Sherman A (2015) Physica Status Solidi (B). doi:10.1002/pssb.201552026Google Scholar
  8. 8.
    Izyumov YA, Skryabin YN (1988) Statistical mechanics of magnetically ordered systems. Consultants Bureau, New YorkGoogle Scholar
  9. 9.
    Gröber C, Eder R, Hanke W (2000) Phys Rev B 62:4336ADSCrossRefGoogle Scholar
  10. 10.
    Gros C (1994) Phys Rev B 50:7295ADSCrossRefGoogle Scholar
  11. 11.
    Sherman A, Schreiber M (2007) Phys Rev B 76:245112; 77:155117 (2008)Google Scholar
  12. 12.
    Hubbard J (1963) Proc R Soc Lond A 276:238; 277:237 (1964)Google Scholar
  13. 13.
    Varney CN et al. (2009) Phys Rev B 80:075116ADSCrossRefGoogle Scholar
  14. 14.
    Haas S, Moreo A, Dagotto E (1995) Phys Rev Lett 74:4281ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of TartuTartuEstonia

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