The European Physical Journal Special Topics

, Volume 226, Issue 12, pp 2751–2762 | Cite as

Two-body bound and edge states in the extended SSH Bose-Hubbard model

  • M. Di LibertoEmail author
  • A. Recati
  • I. Carusotto
  • C. Menotti
Regular Article
Part of the following topical collections:
  1. Quantum Gases and Quantum Coherence


We study the bosonic two-body problem in a Su-Schrieffer-Heeger dimerized chain with on-site and nearest-neighbor interactions. We find two classes of bound states. The first, similar to the one induced by on-site interactions, has its center of mass on the strong link, whereas the second, existing only thanks to nearest-neighbor interactions, is centered on the weak link. We identify energy crossings between these states and analyse them using exact diagonalization and perturbation theory. In the presence of open boundary conditions, novel strongly-localized edge-bound states appear in the spectrum as a consequence of the interplay between lattice geometry, on-site and nearest-neighbor interactions. Contrary to the case of purely on-site interactions, such EBS persist even in the strongly interacting regime.


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  1. 1.
    D.C. Mattis. Rev. Mod. Phys. 58, 361 (1986)ADSCrossRefGoogle Scholar
  2. 2.
    K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A.J. Daley, A. Kantian, H.P. Büchler, P. Zoller, Nature 441, 853 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    J.H. Denschlag, A.J. Daley, Proceedings of the international school of physics, Enrico Fermi, Course CLXIV, Ultra-Cold Fermi Gases (2006)Google Scholar
  4. 4.
    M. Valiente, D. Petrosyan, J. Phys. B: At. Mol. Opt. Phys. 42, 121001 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    M. Valiente. Phys. Rev. A 81, 042102 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    M. Valiente, K. Mølmer. Phys. Rev. A 84, 053628 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    C. Menotti, F. Minganti, A. Recati, Phys. Rev. A 93, 033602 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    V. Alba, K. Saha, M. Haque, J. Stat. Mech. P10018 (2013)Google Scholar
  9. 9.
    M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)ADSCrossRefGoogle Scholar
  11. 11.
    C.-K. Chiu, J.C.Y. Teo, A.P. Schnyder, S. Ryu, Rev. Mod. Phys. 88, 035005 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    M. Di Liberto, A. Recati, I. Carusotto, C. Menotti, Phys. Rev. A 94, 062704 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    M.A. Gorlach, A.N. Poddubny, arXiv:1608.02093
  14. 14.
    M.A. Gorlach, A.N. Poddubny, Phys. Rev. A 95, 033831 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    M. Bello, C.E. Creffield, G. Platero, Scientific Rep. 6, 22562 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    M. Bello, C.E. Creffield, G. Platero, Phys. Rev. B 95, 094303 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    A.M. Marques, R.G. Dias, Phys. Rev. B 95, 115443 (2017)ADSCrossRefGoogle Scholar
  18. 18.
    X. Qin, F. Mei, F. Ke, L. Zhang, C. Lee, arXiv:1611.00205 (2016)
  19. 19.
    M. Eric Tai, A. Lukin, M. Rispoli, R. Schittko, T. Menke, D. Borgnia, P.M. Preiss, F. Grusdt, A.M. Kaufman, M. Greiner, arXiv:1612.05631
  20. 20.
    I. Tamm, Z. Sowjetunion, Physics 1, 733 (1932)Google Scholar
  21. 21.
    W. Shockley, Phys. Rev. 56, 317 (1939)ADSCrossRefGoogle Scholar
  22. 22.
    S. Longhi, Opt. Lett. 36, 3248 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, Nat. Commun. 4, 1555 (2013)CrossRefGoogle Scholar
  24. 24.
    A. Schreiber, A. Gábris, P.P. Rohde, K. Laiho, M. Štefaňák, V. Potoček, C. Hamilton, I. Jex, C. Silberhorn, Science 336, 55 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    S. Mukherjee, A. Spracklen, D. Choudhury, N. Goldman, P. Öhberg, E. Andersson, R.R. Thomson, N. J. Phys. 17 115002 (2015)CrossRefGoogle Scholar
  26. 26.
    S. Mukherjee, M. Valiente, N. Goldman, A. Spracklen, E. Andersson, P. Öhberg, R.R. Thomson, Phys. Rev. A 94, 053853 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    S. Baier, M.J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, F. Ferlaino, Science 352, 201 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)ADSCrossRefGoogle Scholar
  29. 29.
    M. Valiente, M. Küster, A. Saenz, Europhys. Lett. 92, 10001 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    C. Cohen-Tannoudji, J. Dupont-Roc, G.G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (John Wiley & Sons, Inc., 1998)Google Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • M. Di Liberto
    • 1
    Email author
  • A. Recati
    • 1
    • 2
  • I. Carusotto
    • 1
  • C. Menotti
    • 1
  1. 1.INO-CNR BEC Center and Dipartimento di Fisica, Università di TrentoPovoItaly
  2. 2.Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität MünchenMünchenGermany

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