Ground-State Properties for Bilayer Kitaev Model: Dimer Expansion Study

  • Akihisa KogaEmail author
  • Hiroyuki Tomishige
  • Joji Nasu
Original Paper


We study ground-state properties in the bilayer Kitaev model by means of the dimer expansion. The existence of parity symmetries in the system reduces the computational cost significantly. This allows us to expand the ground-state energy and interlayer spin-spin correlation up to the 30th order in the interdimer Kitaev coupling. The numerical calculations clarify that the dimer singlet state is indeed realized in the wide parameter region.


Bilayer Kitaev model Dimer expansion 



This work is financially supported by Grant-in-Aid for Scientific Research from JSPS, KAKENHI Grant nos. JP17K05536, JP18K04678 (A.K.) and JP16K17747, JP16H02206, and JP16H00987 (J.N.). Parts of the numerical calculations were performed in the supercomputing systems in ISSP, the University of Tokyo.


  1. 1.
    Shastry, B.S., Sutherland, B.: Physica 108B, 1069 (1981)Google Scholar
  2. 2.
    Miyahara, S., Ueda, K.: Phys. Rev. Lett. 82, 3701 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    Koga, A., Kawakami, N.: Phys. Rev. Lett. 84, 4461 (2000)ADSCrossRefGoogle Scholar
  4. 4.
    Haravifard, S., Graf, D., Feiguin, A.E., Batista, C.D., Lang, J.C., Silevitch, D.M., Srajer, G., Gaulin, B.D., Dabkowska, H.A., Rosenbaum, T.F.: Nat. Comm. 7, 11956 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    Zayed, M.E., et al.: Nat. Phys. 13, 962 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Sakurai, T., Hirao, Y., Hijii, K., Okubo, S., Ohta, H., Uwatoko, Y., Kudo, K., Koike, Y.: Phys. J. Soc. Jpn. 87, 033701 (2018)ADSCrossRefGoogle Scholar
  7. 7.
    Kageyama, H., Yoshimura, K., Stern, R., Mushnikov, N.V., Onizuka, K., Kato, M., Kosuge, K., Slichter, C.P., Goto, T., Ueda, Y.: Phys. Rev. Lett. 82, 3168 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    Takushima, Y., Koga, A., Kawakami, N.: Phys. J. Soc. Jpn. 70, 1369 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Kitaev, A.: Ann. Phys. (N. Y.) 321, 2 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    Feng, X.Y., Zhang, G.M., Xiang, T.: Phys. Rev. Lett. 98, 087204 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    Chen, H.D., Hu, J.: Phys. Rev. B 76, 193101 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Chen, H.D., Nussinov, Z.: J. Phys. A 41, 075001 (2008)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Koga, A., Tomishige, H., Nasu, J.: J. Phys. Soc. Jpn. 87(6), 063703 (2018)ADSCrossRefGoogle Scholar
  14. 14.
    Nasu, J., Udagawa, M., Motome, Y.: Phys. Rev. B 92, 115122 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    Yamaji, Y., Suzuki, T., Yamada, T., Suga, S.I, Kawashima, N., Imada, M.: Phys. Rev. B 93, 174425 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    Yoshitake, J., Nasu, J., Motome, Y.: Phys. Rev. Lett. 117, 157203 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    Nasu, J., Yoshitake, J., Motome, Y.: Phys. Rev. Lett. 119, 127204 (2017)ADSCrossRefGoogle Scholar
  18. 18.
    Suzuki, T., Suga, S.I.: Phys. Rev. B 97, 134424 (2018)ADSCrossRefGoogle Scholar
  19. 19.
    Yamaji, Y., Suzuki, T., Kawamura, M.: arXiv:1802.02854 (unpublished)
  20. 20.
    Koga, A., Nakauchi, S., Nasu, J.: Phys. Rev. B 97, 094427 (2018)ADSCrossRefGoogle Scholar
  21. 21.
    Tomishige, H., Nasu, J., Koga, A.: Phys. Rev. B 97, 094403 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    Guttmann, A.J.: Phase Transitions and Critical Phenomena, vol. 13. Academic, New York (1989)Google Scholar
  23. 23.
    Singh, R., Gelfand, M., Huse, D.A.: Phys. Rev. Lett. 61, 2484 (1988)ADSCrossRefGoogle Scholar
  24. 24.
    Gelfand, M., Singh, R., Huse, D.A.: J. Stat. Phys. 59, 1093 (1996)ADSCrossRefGoogle Scholar
  25. 25.
    Gelfand, M.: Solid State Commun. 98, 11 (1996)ADSCrossRefGoogle Scholar
  26. 26.
    Sushkov, O.P., Oitmaa, J., Weihong, Z.: Phys. Rev. B 63, 104420 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    Koga, A.: J. Phys. Soc. Jpn. 69, 3509 (2000)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Singh, R.R.P., Oitmaa, J.: Phys. Rev. B 96, 144414 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    Hida, K.: J. Phys. Soc. Jpn. 61, 1013 (1992)ADSCrossRefGoogle Scholar
  30. 30.
    Hida, K.: J. Phys. Soc. Jpn. 67, 1540 (1998)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of PhysicsTokyo Institute of TechnologyMeguroJapan

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