Advertisement

Hamiltonian Flow in Condensed Matter Physics

  • F. Wegner
Part of the Centre de Physique des Houches book series (LHWINTER, volume 8)

Abstract

A recently developed method to diagonalize or block-diagonalize Hamiltoni-ans by means of an appropriate continuous unitary transformation is reviewed. Two applications in condensed matter physics are given as examples: (i) the interaction of an n-orbital model of fermions in the limit of large n is brought to block-diagonal form, and (ii) the generation of the effective attractive two-electron interaction due to the elimination of electron-phonon interaction is given. The advantage of this method in particular in comparison to conventional perturbation theory is pointed out.

Keywords

Occupation Number Diagonal Part Diagonal Matrix Element HAMILTONIAN Flow Matrix Element Versus 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Wegner F., Ann. Phys. (Leipzig) 3 (1994) 77.ADSzbMATHGoogle Scholar
  2. [2]
    Glazek S.D. and Wilson K.G., Phys. Rev. D48 (1993) 5863.ADSGoogle Scholar
  3. [3]
    Wilson K.G., Walhout T.S., Harindranath A., Zhang W.M., Perry R.J. and Glazek S.D., Phys. Rev. D49 (1994) 6720.MathSciNetADSGoogle Scholar
  4. [4]
    Kehrein S.K. and Mielke A., J. Phys. A27 (1994) 4259, 5705.MathSciNetADSzbMATHGoogle Scholar
  5. [5]
    Kehrein S.K. and Mielke A., Ann. Phys. (NY) 252 (1996) 1.ADSCrossRefGoogle Scholar
  6. [6]
    Kehrein S., Mielke A. and Neu P., Z. Phys. B99 (1996) 269.CrossRefGoogle Scholar
  7. [7]
    Kehrein S.K. and Mielke A., Phys. Lett. A219 (1996) 313.CrossRefGoogle Scholar
  8. [8]
    Lenz P. and Wegner F., Nucl. Phys. B482 (1996) 693.ADSCrossRefGoogle Scholar
  9. [9]
    Fröhlich H., Proc. Roy. Soc. London A215 (1952) 291.ADSzbMATHCrossRefGoogle Scholar
  10. [10]
    Mielke A., Ann. Physik (Leipzig) 6 (1997) 215.MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. [11]
    Mielke A., Calculating critical temperatures of superconductivity from a renormalized Hamiltonian, preprint, 1997.Google Scholar
  12. [12]
    Eliashberg G.M., Zh. Eksp. Teor. Fiz. 28 (1960) 966;Google Scholar
  13. [12a]
    Eliashberg G.M., Zh. Eksp. Teor. Fiz. 29 (1960) 1437Google Scholar
  14. [12b]
    Eliashberg G.M., [Sov. Physics JETP 11, 696; 12, 1000].Google Scholar
  15. [13]
    MacMillan W., Phys. Rev. 167 (1968) 331.ADSCrossRefGoogle Scholar
  16. [14]
    Luttinger J.M., J. Math. Phys. 4 (1963) 1154.MathSciNetADSCrossRefGoogle Scholar
  17. [15]
    Kabel A. and Wegner F., to appear in Z. Physik B (1997).Google Scholar
  18. [16]
    Stein J., Flow equations and the strong-coupling expansion for the Hubbard Model, to appear in J. Stat. Phys. (1996).Google Scholar
  19. [17]
    Kehrein S.K. and Mielke A., Ann. Phys. (Leipzig) 6 (1997) 90.MathSciNetADSzbMATHGoogle Scholar
  20. [18]
    Kehrein S.K. and Mielke A., Diagonalization of system plus environment Hamiltonians, preprint cond-mat/9701123.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • F. Wegner
    • 1
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergGermany

Personalised recommendations