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Variational Monte-Carlo study of the extended Bose-Hubbard model with short- and infinite-range interactions

  • Benjamin BognerEmail author
  • Clément De Daniloff
  • Heiko Rieger
Regular Article
  • 72 Downloads

Abstract

In this paper, we study the two-dimensional Bose-Hubbard model with short- and long-range interactions in the canonical ensemble. Using a Variational Monte-Carlo method, we obtain the phase diagrams containing four different phases: Mott insulator, density wave, superfluid and supersolid. The transition lines are determined using the structure factor and the superfluid density. We observe that the phase diagrams for short and long-range interactions are very similar quantitatively and qualitatively, but show also some significant differences. To evaluate the quality of our Variational approach, we compare our results with results published by other groups, obtained with various methods, such as an exact quantum Monte-Carlo algorithm and Gutzwiller Ansatz.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    M.P. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989) ADSCrossRefGoogle Scholar
  2. 2.
    V.A. Kashurnikov, B.V. Svistunov, Phys. Rev. B 53, 11776 (1996) ADSCrossRefGoogle Scholar
  3. 3.
    G.G. Batrouni, R.T. Scalettar, G.T. Zimanyi, Phys. Rev. Lett. 65, 1765 (1990) ADSCrossRefGoogle Scholar
  4. 4.
    G.G. Batrouni, R.T. Scalettar, Phys. Rev. B 46, 9051 (1992) ADSCrossRefGoogle Scholar
  5. 5.
    W. Krauth, N. Trivedi, Europhys. Lett. 14, 627 (1991) ADSCrossRefGoogle Scholar
  6. 6.
    W. Krauth, N. Trivedi, D. Ceperley, Phys. Rev. Lett. 67, 2307 (1991) ADSCrossRefGoogle Scholar
  7. 7.
    D.M. Ceperley, Rev. Mod. Phys. 67, 279 (1995) ADSCrossRefGoogle Scholar
  8. 8.
    N. Prokof’ev, B. Svistunov, I. Tupitsyn, Phys. Lett. A 238, 253 (1998) ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    N. Prokof’ev, B. Svistunov, Phys. Rev. Lett. 87, 160601 (2001) ADSCrossRefGoogle Scholar
  10. 10.
    N. Prokof’ev, B. Svistunov, Phys. Rev. Lett. 92, 015703 (2004) ADSCrossRefGoogle Scholar
  11. 11.
    N. Kawashima, K. Harada, J. Phys. Soc. Jpn. 73, 1379 (2004) ADSCrossRefGoogle Scholar
  12. 12.
    M. Boninsegni, N.V. Prokof’ev, B.V. Svistunov, Phys. Rev. E 74, 036701 (2006) ADSCrossRefGoogle Scholar
  13. 13.
    V.G. Rousseau, Phys. Rev. E 77, 056705 (2008) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    V.G. Rousseau, Phys. Rev. E 78, 056707 (2008) ADSCrossRefGoogle Scholar
  15. 15.
    F. Alet, E.S. Sørensen, Phys. Rev. B 70, 024513 (2004) ADSCrossRefGoogle Scholar
  16. 16.
    M. Köhl, H. Moritz, T. Stöferle, C. Schori, T. Esslinger, J. Low Temp. Phys. 138, 635 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    B. Capogrosso-Sansone, N.V. Prokof’ev, B.V. Svistunov, Phys. Rev. B 75, 134302 (2007) ADSCrossRefGoogle Scholar
  18. 18.
    B. Capogrosso-Sansone, S.G. Söyler, N. Prokof’ev, B. Svistunov, Phys. Rev. A 77, 015602 (2008) ADSCrossRefGoogle Scholar
  19. 19.
    T. Ohgoe, T. Suzuki, N. Kawashima, Phys. Rev. B 86, 054520 (2012) ADSCrossRefGoogle Scholar
  20. 20.
    E. Duchon, N. Trivedi, Ann. Phys. 525, L35 (2013) ADSCrossRefGoogle Scholar
  21. 21.
    S.R. White, Phys. Rev. Lett. 69, 2863 (1992) ADSCrossRefGoogle Scholar
  22. 22.
    W. Krauth, M. Caffarel, J.P. Bouchaud, Phys. Rev. B 45, 3137 (1992) ADSCrossRefGoogle Scholar
  23. 23.
    N. Elstner, H. Monien, Phys. Rev. B 59, 12184 (1999) ADSCrossRefGoogle Scholar
  24. 24.
    T.D. Kühner, H. Monien, Phys. Rev. B 58, R14741 (1998) ADSCrossRefGoogle Scholar
  25. 25.
    T.D. Kühner, S.R. White, H. Monien, Phys. Rev. B 61, 12474 (2000) ADSCrossRefGoogle Scholar
  26. 26.
    T. Kimura, Phys. Rev. A 84, 063630 (2011) ADSCrossRefGoogle Scholar
  27. 27.
    K. Kawaki, Y. Kuno, I. Ichinose, Phys. Rev. B 95, 195101 (2017) ADSCrossRefGoogle Scholar
  28. 28.
    D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998) ADSCrossRefGoogle Scholar
  29. 29.
    M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002) ADSCrossRefGoogle Scholar
  30. 30.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008) ADSCrossRefGoogle Scholar
  31. 31.
    H. Ritsch, P. Domokos, F. Brennecke, T. Esslinger, Rev. Mod. Phys. 85, 553 (2013) ADSCrossRefGoogle Scholar
  32. 32.
    O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D.S. Lühmann, B.A. Malomed, T. Sowiński, J. Zakrzewski, Rep. Prog. Phys 78, 066001 (2015) ADSCrossRefGoogle Scholar
  33. 33.
    G.G. Batrouni, R.T. Scalettar, G.T. Zimanyi, A.P. Kampf, Phys. Rev. Lett. 74, 2527 (1995) ADSCrossRefGoogle Scholar
  34. 34.
    M. Boninsegni, N.V. Prokof’ev, Rev. Mod. Phys. 84, 759 (2012) ADSCrossRefGoogle Scholar
  35. 35.
    P. Sengupta, L.P. Pryadko, F. Alet, M. Troyer, G. Schmid, Phys. Rev. Lett. 94, 207202 (2005) ADSCrossRefGoogle Scholar
  36. 36.
    G.G. Batrouni, F. Hébert, R.T. Scalettar, Phys. Rev. Lett. 97, 087209 (2006) ADSCrossRefGoogle Scholar
  37. 37.
    K.W. Mahmud, E.N. Duchon, Y. Kato, N. Kawashima, R.T. Scalettar, N. Trivedi, Phys. Rev. B 84, 054302 (2011) ADSCrossRefGoogle Scholar
  38. 38.
    G.G. Batrouni, R.T. Scalettar, V.G. Rousseau, B. Grémaud, Phys. Rev. Lett. 110, 265303 (2013) ADSCrossRefGoogle Scholar
  39. 39.
    D. Rossini, R. Fazio, New J. Phys 14, 065012 (2012) ADSCrossRefGoogle Scholar
  40. 40.
    B. Grémaud, G.G. Batrouni, Phys. Rev. B 93, 035108 (2016) ADSCrossRefGoogle Scholar
  41. 41.
    A.E. Niederle, H. Rieger, New J. Phys 15, 075029 (2013) ADSCrossRefGoogle Scholar
  42. 42.
    R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, T. Esslinger, Nature 532, 476 (2016) ADSCrossRefGoogle Scholar
  43. 43.
    T. Keller, S.B. Jäger, G. Morigi, J. Stat. Mech. Theory Exp. 2017, 064002 (2017) CrossRefGoogle Scholar
  44. 44.
    Y. Li, L. He, W. Hofstetter, Phys. Rev. A 87, 051604 (2013) ADSCrossRefGoogle Scholar
  45. 45.
    A.E. Niederle, G. Morigi, H. Rieger, Phys. Rev. A 94, 033607 (2016) ADSCrossRefGoogle Scholar
  46. 46.
    N. Dogra, F. Brennecke, S.D. Huber, T. Donner, Phys. Rev. A 94, 023632 (2016) ADSCrossRefGoogle Scholar
  47. 47.
    Y. Chen, Z. Yu, H. Zhai, Phys. Rev. A 93, 041601 (2016) ADSCrossRefGoogle Scholar
  48. 48.
    B. Sundar, E.J. Mueller, Phys. Rev. A 94, 033631 (2016) ADSCrossRefGoogle Scholar
  49. 49.
    T. Flottat, L.d.F. de Parny, F. Hébert, V.G. Rousseau, G.G. Batrouni, Phys. Rev. B 95, 144501 (2017) ADSCrossRefGoogle Scholar
  50. 50.
    H. Habibian, A. Winter, S. Paganelli, H. Rieger, G. Morigi, Phys. Rev. Lett. 110, 075304 (2013) ADSCrossRefGoogle Scholar
  51. 51.
    J. Panas, A. Kauch, K. Byczuk, Phys. Rev. B 95, 115105 (2017) ADSCrossRefGoogle Scholar
  52. 52.
    B. Blaß, H. Rieger, G.m.H. Roósz, F. Iglói, Phys. Rev. Lett. 121, 095301 (2018) ADSCrossRefGoogle Scholar
  53. 53.
    F. Iglói, B. Blaß, G.m.H. Roósz, H. Rieger, Phys. Rev. B 98, 184415 (2018) ADSCrossRefGoogle Scholar
  54. 54.
    M. Capello, F. Becca, M. Fabrizio, S. Sorella, E. Tosatti, Phys. Rev. Lett. 94, 026406 (2005) ADSCrossRefGoogle Scholar
  55. 55.
    L. Cevolani, G. Carleo, L. Sanchez-Palencia, Phys. Rev. A 92, 041603 (2015) ADSCrossRefGoogle Scholar
  56. 56.
    A. van Otterlo, K.H. Wagenblast, R. Baltin, C. Bruder, R. Fazio, G. Schön, Phys. Rev. B 52, 16176 (1995) ADSCrossRefGoogle Scholar
  57. 57.
    K. Yamamoto, S. Todo, S. Miyashita, Phys. Rev. B 79, 094503 (2009) ADSCrossRefGoogle Scholar
  58. 58.
    B. Xi, F. Ye, W. Chen, F. Zhang, G. Su, Phys. Rev. B 84, 054512 (2011) ADSCrossRefGoogle Scholar
  59. 59.
    D.L. Kovrizhin, G.V. Pai, S. Sinha, EPL (Europhysics Letters) 72, 162 (2005) ADSCrossRefGoogle Scholar
  60. 60.
    M. Iskin, Phys. Rev. A 83, 051606 (2011) ADSCrossRefGoogle Scholar
  61. 61.
    S. Rist, C. Menotti, G. Morigi, Phys. Rev. A 81, 013404 (2010) ADSCrossRefGoogle Scholar
  62. 62.
    J.S. Douglas, K. Burnett, Phys. Rev. A 84, 033637 (2011) ADSCrossRefGoogle Scholar
  63. 63.
    W.L. McMillan, Phys. Rev. 138, A442 (1965) ADSCrossRefGoogle Scholar
  64. 64.
    D. Ceperley, G.V. Chester, M.H. Kalos, Phys. Rev. B 16, 3081 (1977) ADSCrossRefGoogle Scholar
  65. 65.
    S. Sorella, Phys. Rev. B 71, 241103 (2005) ADSCrossRefGoogle Scholar
  66. 66.
    J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973) ADSCrossRefGoogle Scholar
  67. 67.
    M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, Phys. Rev. B 63, 214503 (2001) ADSCrossRefGoogle Scholar
  68. 68.
    H. Yokoyama, H. Shiba, J. Phys. Soc. Jpn. 59, 3669 (1990) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Benjamin Bogner
    • 1
    Email author
  • Clément De Daniloff
    • 2
  • Heiko Rieger
    • 1
  1. 1.Theoretical Physics, Saarland UniversitySaarbrückenGermany
  2. 2.École Normale SupérieureParisFrance

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