Spectral Properties of the Bose-Hubbard Model Within the Cluster Perturbation Theory in X-Operators Representation

Abstract

We study the two-dimensional ultracold Bose gas in optical lattice. We use cluster perturbation theory based on Hubbard X-operators to calculate the spectral function and phase diagram of Bose-Hubbard model which is minimal model to describe behavior of ultracold gases in optical lattices. We have analyzed spectral properties of spinless bosons in a square lattice taking into account the short-range correlation.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. 1.

    Johnson, T. H., Clark, S. R., Jaksch, D.: EPJ Quantum Technology 1, 1 (2014)

    Article  Google Scholar 

  2. 2.

    Buluta, I., Nori, F.: Science 326, 108 (2009)

    ADS  Article  Google Scholar 

  3. 3.

    Jaksch, D., Bruder, C., Cirac, J., Gardiner, C., Zoller, P.: Phys. Rev. Lett. 81, 3108 (1998)

    ADS  Article  Google Scholar 

  4. 4.

    Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W., Bloch, I.: Nature 415, 39 (2002)

    ADS  Article  Google Scholar 

  5. 5.

    Spielman, I. B., Phillips, W. D., Porto, J. V.: Phys. Rev. Lett. 98, 080404 (2007)

    ADS  Article  Google Scholar 

  6. 6.

    Spielman, I. B., Phillips, W. D., Porto, J. V.: Phys. Rev. Lett. 100, 120402 (2008)

    ADS  Article  Google Scholar 

  7. 7.

    Bloch, I., Jean, D., Wilhelm, Z.: Rev. Mod. Phys. 80, 885 (2008)

    ADS  Article  Google Scholar 

  8. 8.

    Jiang, L., Rey, A. M., Romero-isart, O., García-ripoll, J. J., Sanpera, A., Lukin, M. D.: Phys. Rev. A 79, 022309 (2009)

    ADS  Article  Google Scholar 

  9. 9.

    Knap, M., Arrigoni, E., Linden, W. V. D.: Phys. Rev. B 81, 024301 (2010)

    ADS  Article  Google Scholar 

  10. 10.

    Zhang, X. h., Kou, S. p.: Int. J. Mod. Phys. B 27(4), 1250214 (2013)

    ADS  Article  Google Scholar 

  11. 11.

    Capogrosso-Sansone, B., Soyler, S. G., Prokof’ev, N., Svistunov, B.: Phys. Rev. A 77, 015602 (2008)

    ADS  Article  Google Scholar 

  12. 12.

    Fisher, M. P. A., Weichman, P. B., Grinstein, G., Fisher, D. S.: Phys. Rev. B 40, 546 (1989)

    ADS  Article  Google Scholar 

  13. 13.

    Nikolaev, S. V., Ovchinnikov, S. G.: J. Exp. Theor. Phys. 111(4), 635 (2010)

    ADS  Article  Google Scholar 

  14. 14.

    Hubbard, J.: Proceedings of the Royal Society A Mathematical. Phys. Eng. Sci. 276, 238 (1963)

    Article  Google Scholar 

  15. 15.

    Ovchinnikov, S., Val’kov, V.: Hubbard Operators in the Theory of Strongly Correlated Electrons. Imperial College Press, London (2004)

    Google Scholar 

  16. 16.

    Elstner, N., Monien, H.: Phys. Rev. B 59(9), 12184 (1999)

    ADS  Article  Google Scholar 

Download references

Acknowledgments

This work was supported by RFBR grant 16-02-00098, Government of Krasnoyarsk Territory and RFBR according to the research projects 16-42-243048, 16-42-240511, and 16-42-240769, and the Russian President Grant NSh-7559.2016.2.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Kirill Kudashkin.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kudashkin, K., Nikolaev, S. & Ovchinnikov, S. Spectral Properties of the Bose-Hubbard Model Within the Cluster Perturbation Theory in X-Operators Representation. J Supercond Nov Magn 30, 103–107 (2017). https://doi.org/10.1007/s10948-016-3781-y

Download citation

Keywords

  • Bose-Hubbard model
  • Ultracold gases
  • Cluster perturbation theory
  • Density of states
  • Spectral properties