Phase diagrams of bosonic ABn chains

  • G. J. Cruz
  • R. Franco
  • J. Silva-Valencia
Regular Article


The A B N − 1 chain is a system that consists of repeating a unit cell with N sites where between the A and B sites there is an energy difference of λ. We considered bosons in these special lattices and took into account the kinetic energy, the local two-body interaction, and the inhomogenous local energy in the Hamiltonian. We found the charge density wave (CDW) and superfluid and Mott insulator phases, and constructed the phase diagram for N = 2 and 3 at the thermodynamic limit. The system exhibited insulator phases for densities ρ = α/N, with α being an integer. We obtained that superfluid regions separate the insulator phases for densities larger than one. For any N value, we found that for integer densities ρ, the system exhibits ρ + 1 insulator phases, a Mott insulator phase, and ρ CDW phases. For non-integer densities larger than one, several CDW phases appear.


Solid State and Materials 


  1. 1.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    I. Bloch, J. Dalibard, S. Nascimbène, Nat. Phys. 8, 267 (2012)CrossRefGoogle Scholar
  3. 3.
    D. Jaksch, C. Bruder, J. Cirac, C. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    M. Atala, M. Aidelsburger, J.T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, I. Bloch, Nat. Phys. 9, 795 (2013)CrossRefGoogle Scholar
  7. 7.
    M. Di Liberto, T. Comparin, T. Kock, M. Ölschläger, A. Hemmerich, C. Morais Smith, Nat. Commun. 5, 5735 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    M. Messer, R. Desbuquois, T. Uehlinger, G. Jotzu, S. Huber, D. Greif, T. Esslinger, Phys. Rev. Lett. 115, 115303 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    P. Buonsante, A. Vezzani, Phys. Rev. A 70, 033608 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    V.G. Rousseau, D.P. Arovas, M. Rigol, F. Hébert, G.G. Batrouni, R.T. Scalettar, Phys. Rev. B 73, 174516 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    A. Dhar, T. Mishra, R.V. Pai, B.P. Das, Phys. Rev. A 83, 053621 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    A. Dhar, M. Singh, R.V. Pai, B.P. Das, Phys. Rev. A 84, 033631 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    M. Singh, A. Dhar, T. Mishra, R.V. Pai, B.P. Das, Phys. Rev. A 85, 051604(R) (2012)ADSCrossRefGoogle Scholar
  14. 14.
    S.R. White, Phys. Rev. Lett. 69, 2863 (1992)ADSCrossRefGoogle Scholar
  15. 15.
    V.V. França, K. Capelle, Phys. Rev. Lett. 100, 070403 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    T.D. Kühner, H. Monien, Phys. Rev. B 58, R14741 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    T.D. Kühner, S.R. White, H. Monien, Phys. Rev. B 61, 12474 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    S. Ejima, H. Fehske, F. Gebhard, Europhys. Lett. 93, 30002 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    S. Yamamoto, Phys. Rev. B 64, 140102(R) (2001)ADSCrossRefGoogle Scholar
  20. 20.
    F.X. Redl, K.S. Cho, C.B. Murray, S. O’Brien, Nature 423, 01702 (2003)CrossRefGoogle Scholar
  21. 21.
    M.E. Torio, A.A. Aligia, G.I. Japaridze, B. Normand, Phys. Rev. B 73, 115109 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    J. Silva-Valencia, A.M.C. Souza, Phys. Rev. A 85, 033612 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    T. Li, H.M. Gou, S. Chen, S.Q. Shen, Phys. Rev. B 91, 134101 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    G.J. Cruz, R. Franco, J. Silva-Valencia, in preparationGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Departamento de Ciencias Básicas, Universidad Santo TomasBogotáColombia
  2. 2.Departamento de Física, Universidad Nacional de ColombiaBogotáColombia

Personalised recommendations