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Communications in Mathematical Physics

, Volume 266, Issue 3, pp 777–795 | Cite as

Mott Transition in Lattice Boson Models

  • R. Fernández
  • J. Fröhlich
  • D. Ueltschi
Article

Abstract

We use mathematically rigorous perturbation theory to study the transition between the Mott insulator and the conjectured Bose-Einstein condensate in a hard-core Bose-Hubbard model. The critical line is established to lowest order in the tunneling amplitude.

Keywords

Partition Function Critical Line Mott Transition Cluster Expansion Mott Insulator 
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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References

  1. 1.
    Aizenman M., Lieb E.H., Seiringer R., Solovej J.P., Yngvason J. (2004). Bose-Einstein quantum phase transition in an optical lattice model. Phys. Rev. A 70:023612; see also cond-mat/0412034; see also http:// arxiv.org/list/cond-mat/0412034, 2004CrossRefADSGoogle Scholar
  2. 2.
    Batrouni G.G., Assaad F.F., Scalettar R.T., Denteneer P.J.H. (2005). Dynamic response of trapped ultracold bosons on optical lattices. Phys. Rev. A 72:031601(R)CrossRefADSGoogle Scholar
  3. 3.
    Borgs C., Kotecký R., Ueltschi D. (1996). Low temperature phase diagrams for quantum perturbations of classical spin systems. Commun. Math. Phys. 181:409–446CrossRefADSzbMATHGoogle Scholar
  4. 4.
    Bru J.-B., Dorlas T.C. (2003). Exact solution of the infinite-range-hopping Bose-Hubbard model. J. Stat. Phys. 113:177–196CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Datta N., Fernández R., Fröhlich J. (1996). Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states. J. Stat. Phys. 84:455–534CrossRefADSzbMATHGoogle Scholar
  6. 6.
    Datta N., Fernández R., Fröhlich J., Rey-Bellet L. (1996). Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy. Helv. Phys. Acta. 69:752–820MathSciNetzbMATHGoogle Scholar
  7. 7.
    Dyson F.J., Lieb E.H., Simon B. (1978). Phase transitions in quantum spin systems with isotropic and nonisotropic interactions. J. Stat. Phys. 18:335–383CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Elstner N., Monien H. (1999). Dynamics and thermodynamics of the Bose-Hubbard model. Phys. Rev. B 59:12184–12187CrossRefADSGoogle Scholar
  9. 9.
    Fisher M.P.A., Weichman P.B., Grinstein G., Fisher D.S. (1989). Boson localization and the superfluid-insulator transition. Phys. Rev. B 40:546–570CrossRefADSGoogle Scholar
  10. 10.
    Freericks J.K., Monien H. (1996). Strong-coupling expansions for the pure and disordered Bose-Hubbard model. Phys. Rev. B 53:2691–2700CrossRefADSGoogle Scholar
  11. 11.
    Fröhlich J., Simon B., Spencer T. (1976). Infrared bounds, phase transitions and continuous symmetry breaking. Commun. Math. Phys. 50:79–95CrossRefADSGoogle Scholar
  12. 12.
    Greiner M., Mandel O., Esslinger T., Hänsch T.W., Bloch I. (2002). Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415:39–44CrossRefADSGoogle Scholar
  13. 13.
    Kennedy T. (1985). Long range order in the anisotropic quantum ferromagnetic Heisenberg model. Commun. Math. Phys. 100:447–462CrossRefADSGoogle Scholar
  14. 14.
    Kennedy T., Lieb E.H., Shastry B.S. (1988). The X-Y model has long-range order for all spins and all dimensions greater than one. Phys. Rev. Lett. 61:2582–2584CrossRefADSGoogle Scholar
  15. 15.
    Kölh M., Moritz H., Stöferle T., Schori C., Esslinger T. (2005). Superfluid to Mott insulator transition in one, two, and three dimensions. J. Low Temp. Phys. 138:635CrossRefADSGoogle Scholar
  16. 16.
    Kotecký R., Ueltschi D. (1999). Effective interactions due to quantum fluctuations. Commun. Math. Phys. 206:289–335CrossRefADSzbMATHGoogle Scholar
  17. 17.
    Lieb E.H., Seiringer R., Solovej J.P., Yngvason J. (2005). The mathematics of the Bose gas and its condensation. Oberwohlfach Seminars, Basel Birkhäuser,Google Scholar
  18. 18.
    Messager A., Miracle-Solé S. (1996). Low temperature states in the Falicov-Kimball model. Rev. Math. Phys. 8:271–99CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    Schmid G., Todo S., Troyer M., Dorneich A. (2002). Finite-temperature phase diagram of hard-core bosons in two dimensions. Phys. Rev. Lett. 88:167208CrossRefADSGoogle Scholar
  20. 20.
    Ueltschi D. (2004). Cluster expansions and correlation functions. Moscow Math. J. 4:511–522MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Raphaël SalemUMR 6085 CNRS-Université de RouenSaint Etienne du RouvrayFrance
  2. 2.Institut für Theoretische PhysikEidgenössische Technische HochschuleZürichSwitzerland
  3. 3.Department of MathematicsUniversity of ArizonaTucsonUSA

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