Skip to main content
SpringerLink
Log in

Revisiting pairing of bosons in one-dimensional Bose–Hubbard model with three-body interaction using CMFT+DMRG method

  • Regular Article - Cold Matter and Quantum Gases
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We revisit the Bose–Hubbard model with hard-core three-body attractive interactions in one-dimension using the cluster mean-field theory with the density-matrix renormalization group. Our study focuses on the region of the phase diagram between density one Mott MI(1) and density three Mott MI(3) insulator lobes and studies the pairing of bosons. We calculate the order parameters and condensate factors corresponding to atomic and pair superfluid phases. We find no phase transition directly from MI(1) to MI(3) when the attractive three-body interaction is present. The pair superfluid dominates the region between MI(1) and MI(3) when the hopping parameter is small. As the hopping parameter increases, the model shows a phase transition to the atomic superfluid. However, the paring of bosons persists even in the atomic superfluid phases. We finally obtain the phase diagram and compare it with earlier results.

Graphical Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request. This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All results can be replicated using the numerical procedures described in the paper.]

References

  1. I. Bloch, J. Dalibard, W. Zwerger, Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008). https://doi.org/10.1103/RevModPhys.80.885

    Article  ADS  Google Scholar 

  2. M. Lewenstein, S. Sanpera, V. Ahufinger, B. Damski, A. (De) Sen, U. Sen, Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007). https://doi.org/10.1080/00018730701223200

    Article  ADS  Google Scholar 

  3. M. Lewenstein, S. Sanpera, V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford University Press, Oxford, 2013)

    Google Scholar 

  4. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsh, I. Bloch, Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002). https://doi.org/10.1038/415039a

    Article  ADS  Google Scholar 

  5. D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998). https://doi.org/10.1103/PhysRevLett.81.3108

    Article  ADS  Google Scholar 

  6. T. Stöferle, H. Moritz, C. Schori, M. Köhl, T. Esslinger, Transition from a strongly interacting 1d superfluid to a mott insulator. Phys. Rev. Lett. 92, 130403 (2004). https://doi.org/10.1103/PhysRevLett.92.130403

    Article  ADS  Google Scholar 

  7. C.D. Fertig, K.M. O’Hara, J.H. Huckans, S.L. Rolston, W.D. Phillips, J.V. Porto, Strongly inhibited transport of a degenerate 1d bose gas in a lattice. Phys. Rev. Lett. 94, 120403 (2005). https://doi.org/10.1103/PhysRevLett.94.120403

    Article  ADS  Google Scholar 

  8. S.G. Jakobs, V. Meden, H. Schoeller, Nonequilibrium functional renormalization group for interacting quantum systems. Phys. Rev. Lett. 99, 150603 (2007). https://doi.org/10.1103/PhysRevLett.99.150603

    Article  ADS  Google Scholar 

  9. E. Haller, R. Hart, M.J. Mark, J.G. Danzl, M. Reichsöllner Gustavsson, M. Dalmonte, G. Pupillo, H.-C. Nägerl, Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons. Nature 466, 597–600 (2010). https://doi.org/10.1038/nature09259

    Article  ADS  Google Scholar 

  10. I.B. Spielman, W.D. Phillips, J.V. Porto, Mott-insulator transition in a two-dimensional atomic Bose gas. Phys. Rev. Lett. 98, 080404 (2007). https://doi.org/10.1103/PhysRevLett.98.080404

    Article  ADS  Google Scholar 

  11. I.B. Spielman, W.D. Phillips, J.V. Porto, Condensate fraction in a 2d Bose gas measured across the Mott-insulator transition. Phys. Rev. Lett. 100, 120402 (2008). https://doi.org/10.1103/PhysRevLett.100.120402

    Article  ADS  Google Scholar 

  12. N. Gemelke, X. Zhang, C.-L. Hung, C. Chin, In-situ observation of incompressible Mott-insulating domains of ultracold atomic gases. Nature 460, 995 (2009). https://doi.org/10.1038/nature08244

    Article  ADS  Google Scholar 

  13. W.S. Bakr, A. Peng, M.E. Tai, R. Ma, J. Simon, S.J.I. Gillen, P. Fölling, L. Fölling Pollet, M. Greiner, Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547 (2010). https://doi.org/10.1126/science.1192368

    Article  ADS  Google Scholar 

  14. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39 (2002). https://doi.org/10.1038/415039a

    Article  ADS  Google Scholar 

  15. S. Trotzky, L. Pollet, F. Gerbier, U. Schnorrberger, I. Bloch, N.V. Prokof’ev, B. Svistunov, M. Troyer, Suppression of the critical temperature for superfluidity near the Mott transition. Nat. Phys. 6, 998 (2010). https://doi.org/10.1038/nphys1799

    Article  Google Scholar 

  16. S. Will, T. Best, U. Schneider, L. Hackermuller, D. Luhmann, I. Bloch, Time-resolved observation of coherent multi-body interactions in quantum phase revivals. Nature 465, 197 (2010). https://doi.org/10.1038/nature09036

    Article  ADS  Google Scholar 

  17. M.J. Mark, E. Haller, K. Lauber, J.G. Danz, A.J. Daley, H.-C. Näger, Precision measurements on a tunable Mott insulator of ultracold atoms. Phys. Rev. Lett. 107, 175301 (2011). https://doi.org/10.1103/PhysRevLett.107.175301

    Article  ADS  Google Scholar 

  18. A.M. Daley, J.M. Taylor, S. Diehl, M. Baranov, P. Zoller, Atomic three-body loss as a dynamical three-body interaction. Phys. Rev. Lett. 102, 040402 (2009). https://doi.org/10.1103/PhysRevLett.102.040402

    Article  ADS  Google Scholar 

  19. M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546 (1989). https://doi.org/10.1103/PhysRevB.40.546

    Article  ADS  Google Scholar 

  20. A. Safavi-Naini, J. Stecher, B. Capogrosso-Sansone, S.T. Rittenhouse, First-order phase transitions in optical lattices with tunable three-body onsite interaction. Phys. Rev. Lett. 109, 135302 (2012). https://doi.org/10.1103/PhysRevLett.109.135302

    Article  ADS  Google Scholar 

  21. M. Singh, S. Greschner, T. Mishra, Anomalous pairing of bosons: effect of multibody interactions in an optical lattice. Phys. Rev. A 98, 023615 (2018). https://doi.org/10.1103/PhysRevA.98.023615

    Article  ADS  Google Scholar 

  22. P.P. Gaude, A. Das, R.V. Pai, Cluster mean field plus density matrix renormalization theory for the Bose Hubbard models. J. Phys. A: Math. Theor. 55, 265004 (2022). https://doi.org/10.1088/1751-8121/ac71e7

    Article  ADS  MathSciNet  Google Scholar 

  23. S. Mondal, A. Kshetrimayum, T. Mishra, Two-body repulsive bound pairs in a multibody interacting Bose–Hubbard model. Phys. Rev. A 102, 023312 (2020). https://doi.org/10.1103/PhysRevA.102.023312

  24. M. Lewenstein, L. Santos, M.A. Baranov, H. Fehrmann, Atomic Bose–Fermi mixtures in an optical lattice. Phys. Rev. Lett. 92, 050401 (2004). https://doi.org/10.1103/PhysRevLett.92.050401

    Article  ADS  Google Scholar 

  25. G.G. Batrouni, R.T. Scalettar, Phase separation in supersolids. Phys. Rev. Lett. 84, 1599–1602 (2000). https://doi.org/10.1103/PhysRevLett.84.1599

    Article  ADS  Google Scholar 

  26. G.G. Batrouni, R.T. Scalettar, G.T. Zimanyi, A.P. Kampf, Supersolids in the Bose–Hubbard Hamiltonian. Phys. Rev. Lett. 74, 2527–2530 (1995). https://doi.org/10.1103/PhysRevLett.74.2527

    Article  ADS  Google Scholar 

  27. B. Song, S. Dutta, S. Bhave, J.-C. Yu, N.E. Carter, Cooper, U. Schneider, Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice. Nat. Phys. 18, 259–264 (2022). https://doi.org/10.1038/s41567-021-01476-w

    Article  Google Scholar 

  28. A. Tokuno, A. Georges, Ground states of a Bose–Hubbard ladder in an artificial magnetic field: field-theoretical approach. New J. Phys. 16, 073005 (2014). https://doi.org/10.1088/1367-2630/16/7/073005

    Article  ADS  Google Scholar 

  29. A. Dhar, T. Mishra, M. Maji, R.V. Pai, S. Mukerjee, A. Paramekanti, Chiral Mott insulator with staggered loop currents in the fully frustrated Bose–Hubbard model. Phys. Rev. B 87, 174501 (2013). https://doi.org/10.1103/PhysRevB.87.174501

    Article  ADS  Google Scholar 

  30. A. Dhar, M. Maji, T. Mishra, R.V. Pai, S. Mukerjee, A. Paramekanti, Bose–Hubbard model in a strong effective magnetic field: emergence of a chiral Mott insulator ground state. Phys. Rev. A 85, 041602 (2012). https://doi.org/10.1103/PhysRevA.85.041602

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Assistance provided by Directorate of Higher Education, Government of Goa, India is acknowledged by the author (AD).

Author information

Author notes

  1. Chetana G. F. Gaonkar, Pallavi P. Gaude and Ananya Das have contributed equally to this work.

Authors and Affiliations

  1. School of Physical and Applied Sciences, Goa University, Taleigao Plateau, Goa, 403206, India

    Chetana G. F. Gaonkar, Pallavi P. Gaude & Ramesh V. Pai

  2. Department of Physics, Parvatibai Chowgule College of Arts and Science, Gogol, Margao, Goa, 403602, India

    Ananya Das

Authors
  1. Chetana G. F. Gaonkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pallavi P. Gaude
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ananya Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ramesh V. Pai
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to the paper.

Corresponding author

Correspondence to Ramesh V. Pai.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gaonkar, C.G.F., Gaude, P.P., Das, A. et al. Revisiting pairing of bosons in one-dimensional Bose–Hubbard model with three-body interaction using CMFT+DMRG method. Eur. Phys. J. D 78, 43 (2024). https://doi.org/10.1140/epjd/s10053-024-00834-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-024-00834-6

Search

Navigation