Skip to main content
SpringerLink
Log in

Phase diagram of the SU(3) Fermi–Hubbard model with next-neighbor interactions

  • Regular Article - Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We explore the zero-temperature phase diagram of a one-dimensional gas composed of three-color fermions, which interact locally and with their next neighbors. Using the density matrix renormalization group method and considering one-third filling, we characterize the ground state for several values of the parameters, finding diverse phases, namely phase separation, spin-density wave, pairing phase, a metallic phase, two different charge-density waves, and a non-separable state with modulation of charge. We show that the von Neumann block entropy and the fidelity susceptibility are useful for estimating the borders between the phases.

Graphic 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
Fig. 10

Similar content being viewed by others

References

  1. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. De Sen, U. Sen, Adv. Phys. 56, 243 (2007)

    Article  ADS  Google Scholar 

  2. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  3. I. Bloch, J. Dalibard, S. Nascimbéne, Nat. Phys. 8, 267 (2012)

    Article  Google Scholar 

  4. M.A. Cazalilla, A.M. Rey, Rep. Prog. Phys. 77, 124401 (2014)

    Article  ADS  Google Scholar 

  5. S. Capponi, P. Lecheminant, K. Totsuka, Ann. Phys. 367, 50 (2016)

    Article  ADS  Google Scholar 

  6. J. Dobrzyniecki, T. Sowiński. arXiv:2001.04223 (2020)

  7. S. Taie, R. Yamazaki, S. Sugawa, Y. Takahashi, Nat. Phys. 8, 825 (2012)

    Article  Google Scholar 

  8. C. Hofrichter, L. Riegger, F. Scazza, M. Höfer, D.R. Fernandes, I. Bloch, S. Fölling, Phys. Rev. X 6, 021030 (2016)

    Google Scholar 

  9. H. Ozawa, S. Taie, Y. Takasu, Y. Takahashi, Phys. Rev. Lett. 121, 225303 (2018)

    Article  ADS  Google Scholar 

  10. G. Pagano, M. Mancini, G. Cappellini, L. Livi, C. Sias, J. Catani, M. Inguscio, L. Fallani, Phys. Rev. Lett. 115, 265301 (2015)

    Article  ADS  Google Scholar 

  11. X. Zhang, M. Bishof, S.L. Bromley, C.V. Kraus, M.S. Safronova, P. Zoller, A.M. Rey, J. Ye, Science 345, 1467 (2014)

    Article  ADS  Google Scholar 

  12. L. Riegger, N.D. Oppong, M. Höfer, D.R. Fernandes, I. Bloch, S. Fölling, Phys. Rev. Lett. 120, 143601 (2018)

    Article  ADS  Google Scholar 

  13. K. Ono, J. Kobayashi, Y. Amano, K. Sato, Y. Takahashi, Phys. Rev. A 99, 032707 (2019)

    Article  ADS  Google Scholar 

  14. G. Pagano, M. Mancini, G. Cappellini, P. Lombardi, F. Schäfer, H. Hu, X.-J. Liu, J. Catani, C. Sias, M. Inguscio, L. Fallani, Nat. Phys. 10, 198 (2014)

    Article  Google Scholar 

  15. B. Song, Y. Yan, C. He, Z. Ren, Q. Zhou, G.-B. Jo. arXiv:1912.12105 (2020)

  16. A.V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P.S. Julienne, J. Ye, P. Zoller, E. Demler, M.D. Lukin, A.M. Rey, Nat. Phys. 6, 289 (2010)

    Article  Google Scholar 

  17. A. Richaud, M. Ferraretto, M. Capone, Phys. Rev. B 103, 205132 (2021)

    Article  ADS  Google Scholar 

  18. R. Assaraf, P. Azaria, M. Caffarel, P. Lecheminant, Phys. Rev. B 60, 2299 (1999)

    Article  ADS  Google Scholar 

  19. K. Buchta, Ö. Legeza, E. Szirmai, J. Sólyom, Phys. Rev. B 75, 155108 (2007)

    Article  ADS  Google Scholar 

  20. S.R. Manmana, K.R.A. Hazzard, G. Chen, A.E. Feiguin, A.M. Rey, Phys. Rev. A 84, 043601 (2011)

    Article  ADS  Google Scholar 

  21. S.S. Chung, P. Corboz, Phys. Rev. B 100, 035134 (2019)

    Article  ADS  Google Scholar 

  22. H. Xu, Z. Zhou, X. Wang, L. Wang, Y. Wang. arXiv:1912.11233 (2019)

  23. T.O. Wehling, E. Şaşıoğlu, C. Friedrich, A.I. Lichtenstein, M.I. Katsnelson, S. Blügel, Phys. Rev. Lett. 106, 236805 (2011)

    Article  ADS  Google Scholar 

  24. R. Pariser, R.G. Parr, J. Chem. Phys. 21, 767 (1953)

    Article  ADS  Google Scholar 

  25. J.A. Pople, Proc. Phys. Soc. 68, 81 (1955)

    Article  ADS  Google Scholar 

  26. A.C. Jacko, H. Feldner, E. Rose, F. Lissner, M. Dressel, R. Valentí, H.O. Jeschke, Phys. Rev. B 87, 155139 (2013)

    Article  ADS  Google Scholar 

  27. V.J. Emery, Highly Conducting One-Dimensional Solids (Springer, Berlin, 1979)

    Google Scholar 

  28. J.E. Hirsch, Phys. Rev. Lett. 53, 2327 (1984)

    Article  ADS  Google Scholar 

  29. H.Q. Lin, J.E. Hirsch, Phys. Rev. B 33, 8155 (1986)

    Article  ADS  Google Scholar 

  30. J.W. Cannon, E. Fradkin, Phys. Rev. B 41, 9435 (1990)

    Article  ADS  Google Scholar 

  31. J.W. Cannon, R.T. Scalettar, E. Fradkin, Phys. Rev. B 44, 5995 (1991)

    Article  ADS  Google Scholar 

  32. X.Z. Yan, Phys. Rev. B 48, 7140 (1993)

    Article  ADS  Google Scholar 

  33. K. Sano, Y. Ono, J. Phys. Soc. Jpn. 63, 1250 (1994)

    Article  ADS  Google Scholar 

  34. P.G.J.V. Dongen, Phys. Rev. B 49, 7904 (1994)

    Article  ADS  Google Scholar 

  35. M. Nakamura, Phys. Rev. B 61, 16377 (2000)

    Article  ADS  Google Scholar 

  36. M. Tsuchiizu, A. Furusaki, Phys. Rev. Lett. 88, 056402 (2002)

    Article  ADS  Google Scholar 

  37. E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)

    Article  ADS  Google Scholar 

  38. P. Sengupta, A.W. Sandvik, D.K. Campbell, Phys. Rev. B 65, 155113 (2002)

    Article  ADS  Google Scholar 

  39. G. Zhang, Phys. Rev. B 68, 153101 (2003)

    Article  ADS  Google Scholar 

  40. A.W. Sandvik, L. Balents, D.K. Campbell, Phys. Rev. Lett. 92, 236401 (2004)

    Article  ADS  Google Scholar 

  41. Y. Zhang, Phys. Rev. Lett. 92, 246404 (2004)

    Article  ADS  Google Scholar 

  42. K.M. Tam, K. Ming, S.W. Tsai, D.K. Campbell, Phys. Rev. Lett. 96, 036408 (2006)

    Article  ADS  Google Scholar 

  43. S. Ejima, S. Nishimoto, Phys. Rev. Lett. 99, 216403 (2007)

    Article  ADS  Google Scholar 

  44. S. Glocke, A. Klümper, J. Sirker, Phys. Rev. B 76, 155121 (2007)

    Article  ADS  Google Scholar 

  45. F. Mancini, F.P. Mancini, Phys. Rev. E 77, 061120 (2008)

    Article  ADS  Google Scholar 

  46. B. Roy, M.S. Foster, Phys. Rev. X 8, 011049 (2018)

    Google Scholar 

  47. A.L. Szabó, B. Roy, Phys. Rev. B 103, 205135 (2021)

    Article  ADS  Google Scholar 

  48. L.M. Sieberer, M.A. Baranov, Phys. Rev. A 84, 063633 (2011)

    Article  ADS  Google Scholar 

  49. J. Levinsen, N.R. Cooper, G.V. Shlyapnikov, Phys. Rev. A 84, 013603 (2011)

    Article  ADS  Google Scholar 

  50. E. Guardado-Sanchez, B.M. Spar, P. Schauss, R. Belyansky, J.T. Young, P. Bienias, A.V. Gorshkov, T. Iadecola, W.S. Bakr. arXiv:2010.05871 (2020)

  51. M. Barbier, S. Hollerith, W. Hofstetter. arXiv:2105.15046 (2021)

  52. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)

    Article  ADS  Google Scholar 

  53. K. Hallberg, Adv. Phys. 55, 477 (2006)

    Article  ADS  Google Scholar 

  54. U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  55. U. Schollwöck, Ann. Phys. 326, 96 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  56. M. Fishman, S.R. White, E.M. Stoudenmire. The ITensor Software Library for Tensor Network Calculations (2020). arXiv:2007.14822

  57. A. Moreno, A. Muramatsu, S.R. Manmana, Phys. Rev. B 83, 205113 (2011)

    Article  ADS  Google Scholar 

  58. S.R. Manmana, M. Möller, R. Gezzi, K.R.A. Hazzard, Phys. Rev. A 96, 043618 (2017)

    Article  ADS  Google Scholar 

  59. S. Capponi, G. Roux, P. Lecheminant, P. Azaria, E. Boulat, S.R. White, Phys. Rev. A 77, 013624 (2008)

    Article  ADS  Google Scholar 

  60. J. Silva-Valencia, E. Miranda, Phys. Rev. B 65, 024443 (2001)

    Article  ADS  Google Scholar 

  61. J. Silva-Valencia, E. Miranda, R.R.D. Santos, J. Phys. Condens. Matter 13, L619 (2001)

    Article  Google Scholar 

  62. H. Tajima, S. Tsutsui, T.M. Doi, K. Iida. arXiv:2012.03627 (2020)

  63. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    Article  ADS  Google Scholar 

  64. N. Laflorencie, Phys. Rep. 643, 1 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  65. R. Islam, R. Ma, P.M. Preiss, M.E. Tai, A. Lukin, M. Rispoli, M. Greiner, Nature 528, 77 (2015)

    Article  ADS  Google Scholar 

  66. E. Cornfeld, E. Sela, M. Goldstein, Phys. Rev. A 99, 062309 (2019)

    Article  ADS  Google Scholar 

  67. S.-J. Gu, S.-S. Deng, Y.-Q. Li, H.-Q. Lin, Phys. Rev. Lett. 93, 086402 (2004)

    Article  ADS  Google Scholar 

  68. S.-S. Deng, S.-J. Gu, H.-Q. Lin, Phys. Rev. B 74, 045103 (2006)

    Article  ADS  Google Scholar 

  69. C. Mund, Ö. Legeza, R.M. Noack, Phys. Rev. B 79, 245130 (2009)

    Article  ADS  Google Scholar 

  70. F. Iemini, T.O. Maciel, R.O. Vianna, Phys. Rev. B 92, 075423 (2015)

    Article  ADS  Google Scholar 

  71. J. Spalding, S.-W. Tsai, D.K. Campbell, Phys. Rev. B 99, 195445 (2019)

    Article  ADS  Google Scholar 

  72. V.V. França, K. Capelle, Phys. Rev. Lett. 100, 070403 (2008)

    Article  ADS  Google Scholar 

  73. J.J. Mendoza-Arenas, R. Franco, J. Silva-Valencia, Phys. Rev. A 81, 062310 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

J.S.-V. acknowledges helpful discussions with J. J. Mendoza-Arenas. The authors are thankful to Örs Legeza, who provided data for comparison. This research was supported by DIEB- Universidad Nacional de Colombia (Grant no. 51116).

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad Nacional de Colombia, A. A. 5997, Bogotá, Colombia

    A. Pérez-Romero, R. Franco & J. Silva-Valencia

Authors
  1. A. Pérez-Romero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Franco
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Silva-Valencia
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

AP-R programmed the DMRG code and carried out the calculations. RF contributed to the discussions. JS-V planned and designed the study. All contributed to writing the paper.

Corresponding author

Correspondence to J. Silva-Valencia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pérez-Romero, A., Franco, R. & Silva-Valencia, J. Phase diagram of the SU(3) Fermi–Hubbard model with next-neighbor interactions. Eur. Phys. J. B 94, 229 (2021). https://doi.org/10.1140/epjb/s10051-021-00242-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00242-4

Search

Navigation