Skip to main content
Springer Nature Link
Log in

Spin-Liquid Phase in the Hubbard Model on the Honeycomb Lattice

  • Conference paper
High Performance Computing in Science and Engineering '10

  • 2021 Accesses

Abstract

The Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin- \(\frac{1}{2}\) fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Z.Y. Meng et al., Nature 464, 847 (2010).

    Article  Google Scholar 

  2. J. Engel and S. Wessel, Phys. Rev. B 80, 094404 (2009).

    Article  Google Scholar 

  3. T. Fabritius, N. Laflorencie, and S. Wessel, subm. to Phys. Rev. B (2009).

    Google Scholar 

  4. A. Honecker and S. Wessel, Cond. Mat. Phys. 12, 399 (2009).

    Google Scholar 

  5. S. Wessel, Phys. Rev. B 81, 052405 (2010).

    Article  Google Scholar 

  6. F. Heidrich-Meisner et al., Phys. Rev. A 80, 041603(R) (2009).

    Article  Google Scholar 

  7. P.W. Anderson, Mater. Res. Bull. 8, 153 (1973).

    Article  Google Scholar 

  8. P. Fazekas and P.W. Anderson, Philos. Mag. 30, 423 (1974).

    Article  Google Scholar 

  9. P.W. Anderson, Science 235, 1196 (1987).

    Article  Google Scholar 

  10. S.A. Kivelson, D.S. Rokhsar, and J.P. Sethna, Phys. Rev. B 35, 8865 (1987).

    Article  Google Scholar 

  11. E. Manousakis, Rev. Mod. Phys. 63, 1 (1991).

    Article  Google Scholar 

  12. B. Bernu, P. Lecheminant, C. Lhuillier, and L. Pierre, Phys. Rev. B 50, 10048 (1994).

    Article  Google Scholar 

  13. J.D. Reger, J.A. Riera, and A.P. Young, J. Phys.: Condens. Matter 1, 1855 (1989).

    Article  Google Scholar 

  14. J.E. Hirsch, Phys. Rev. B 31, 4403 (1985).

    Article  Google Scholar 

  15. S.R. White et al., Phys. Rev. B 40, 506.

    Google Scholar 

  16. T. Mizusaki and M. Imada, Phys. Rev. B 74, 014421 (2006).

    Article  Google Scholar 

  17. T. Yoshioka, A. Koga, and N. Kawakami, Phys. Rev. Lett. 103, 036401 (2009).

    Article  Google Scholar 

  18. S. Sorella and E. Tosatti, Europhys. Lett. 19, 699 (1992).

    Article  Google Scholar 

  19. L.M. Martelo, M. Dzierzawa, L. Siffert, and D. Baeriswyl, Z. Phys. B 103, 335 (1997).

    Article  Google Scholar 

  20. N. Furukawa, J. Phys. Soc. Jpn. 70, 1483 (2001).

    Article  Google Scholar 

  21. T. Paiva et al., Phys. Rev. B 72, (2005).

    Google Scholar 

  22. M. Bercx, T.C. Lang, and F.F. Assaad, Phys. Rev. B 80, 045412 (2009).

    Article  Google Scholar 

  23. S.-S. Lee and P.A. Lee, Phys. Rev. Lett. 95, 036403 (2005).

    Article  Google Scholar 

  24. I.F. Herbut, Phys. Rev. Lett. 97, 146401 (2006).

    Article  Google Scholar 

  25. M. Hermele, Phys. Rev. B 76, 035125 (2007).

    Article  Google Scholar 

  26. S. Hands and C. Strouthos, Phys. Rev. B 78, 165423 (2008).

    Article  Google Scholar 

  27. J.E. Drut and T.A. Lähde, Phys. Rev. Lett. 102, 026802 (2009).

    Article  Google Scholar 

  28. J.E. Drut and T.A. Lähde, Phys. Rev. B 79, 165425 (2009).

    Article  Google Scholar 

  29. C. Honerkamp, Phys. Rev. Lett. 100, 146404 (2008).

    Article  Google Scholar 

  30. S. Raghu, X.-L. Qi, C. Honerkamp, and S.-C. Zhang, Phys. Rev. Lett. 100, 156401 (2008).

    Article  Google Scholar 

  31. C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005).

    Article  Google Scholar 

  32. X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Phys. Rev. B 74, 085308 (2006).

    Article  Google Scholar 

  33. A.M. Black-Schaffer and S. Doniach, Phys. Rev. B 75, 134512 (2007).

    Article  Google Scholar 

  34. B. Uchoa and A.H.C. Neto, Phys. Rev. Lett. 98, 146801 (2007).

    Article  Google Scholar 

  35. N.B. Kopnin and E.B. Sonin, Phys. Rev. Lett. 100, (2008).

    Google Scholar 

  36. P. Sahebsara and D. Senechal, arXiv:0908.0474 (2009).

  37. F.F. Assaad and H.G. Evertz, Computational Many-Particle Physics, Lecture Notes in Physics 739 (Springer-Verlag, Berlin, 2008), p. 277.

    Book  Google Scholar 

  38. F.F. Assaad, W. Hanke, and D.J. Scalapino, Phys. Rev. Lett. 71, 1915 (1993).

    Article  Google Scholar 

  39. F.F. Assaad, W. Hanke, and D.J. Scalapino, Phys. Rev. B 49, 4327 (1994).

    Article  Google Scholar 

  40. N. Byers and C.N. Yang, Phys. Rev. Lett. 7, 46 (1961).

    Article  Google Scholar 

  41. P. Gegenwart, Q.M. Si, and F. Steglich, Nature Physics 4, 186 (2008).

    Article  Google Scholar 

  42. J.B. Fouet, P. Sindzingre, and C. Lhuillier, Eur. Phys. J. B 20, 241 (2001).

    Article  Google Scholar 

  43. J.T. Chayes, L. Chayes, and S.A. Kivelson, Commun. Math. Phys. 123, 53 (1989).

    Article  MathSciNet  Google Scholar 

  44. S. Cahangirov et al., Phys. Rev. Lett. 102, 236804 (2009).

    Article  Google Scholar 

  45. H. Nakano et al., Angew. Chem. 118, 6451 (2006).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik III, Universität Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    Z. Y. Meng, S. Wessel & A. Muramatsu

  2. Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    T. C. Lang & F. F. Assaad

Authors
  1. Z. Y. Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. C. Lang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Wessel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. F. Assaad
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Muramatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Zentrum für Informationsdienste und, Hochleistungsrechnen (ZIH), TU Dresden, Dresden, 01062, Germany

    Wolfgang E. Nagel

  2. , Abt. Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Str. 10, Freiburg, 79104, Germany

    Dietmar B. Kröner

  3. Stuttgart (HLRS), Universität Stuttgart, Höchstleistungsrechenzentrum, Nobelstraße 19, Stuttgart, 70569, Germany

    Michael M. Resch

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Meng, Z.Y., Lang, T.C., Wessel, S., Assaad, F.F., Muramatsu, A. (2011). Spin-Liquid Phase in the Hubbard Model on the Honeycomb Lattice. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering '10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15748-6_1

Download citation

Publish with us

Policies and ethics