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Properties of Hubbard models with degenerate localised single-particle eigenstates

  • A. MielkeEmail author
Regular Article

Abstract

We consider the repulsive Hubbard model on a class of lattices or graphs for which there is a large degeneracy of the single-particle ground states and where the projector onto the space of single-particle ground states is highly reducible. This means that one can find a basis in the space of the single-particle ground states such that the support of each single-particle ground state belongs to some small cluster and these clusters do not overlap. We show how such lattices can be constructed in arbitrary dimensions. We construct all multi-particle ground states of these models for electron numbers not larger than the number of localised single-particle eigenstates. We derive some of the ground state properties, esp. the residual entropy, i.e. the finite entropy density at zero temperature.

Keywords

Solid State and Materials 

References

  1. 1.
    A. Mielke, J. Phys. A Math. Gen. 24, 3311 (1991) MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    H. Tasaki, Phys. Rev. Lett. 69, 1608 (1992) MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    A. Mielke, H. Tasaki, Commun. Math. Phys. 158, 341 (1993) MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    H. Tasaki, J. Stat. Phys. 84, 535 (1996)MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    A. Tanaka, H. Ueda, Phys. Rev. Lett. 90, 067204 (2003) ADSCrossRefGoogle Scholar
  6. 6.
    A. Mielke, Phys. Rev. Lett. 82, 4312 (1999) ADSCrossRefGoogle Scholar
  7. 7.
    A. Mielke, J. Phys. A Math. Gen. 32, 8411 (1999) MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    C.D. Batista, B.S. Shastry, Phys. Rev. Lett. 91, 116401 (2003) ADSCrossRefGoogle Scholar
  9. 9.
    O. Derzhko, A. Honecker, J. Richter, Phys. Rev. B 79, 054403 (2009) ADSCrossRefGoogle Scholar
  10. 10.
    M. Maksymenko, O. Derzhko, J. Richter, Eur. Phys. J. B 84, 397 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    H.J. Schmidt, J. Richter, R. Moessner, J. Phys. A Math. Gen. 39, 10673 (2006) MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. 12.
    Z. Gulácsi, A. Kampf, D. Vollhardt, Prog. Theor. Phys. Suppl. 176, 1 (2008)zbMATHCrossRefGoogle Scholar
  13. 13.
    A. Mielke, H. Tasaki, preprint (1996), arXiv: cond-mat/9606115Google Scholar
  14. 14.
    M. Aizenman, E.H. Lieb, J. Stat. Phys. 24, 279 (1981)MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    S. Huber, E. Altman, Phys. Rev. B 82, 184502 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikRuprecht Karls UniversitätHeidelbergGermany

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