Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

Regular Article
  • 1 Downloads

Abstract

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ(ω) = (iωL)−1 and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ−1. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    S. Gazit, D. Podolsky, A. Auerbach, D.P. Arovas, Phys. Rev. B 88, 235108 (2013) ADSCrossRefGoogle Scholar
  2. 2.
    A.V. Chubukov, S. Sachdev, J. Ye, Phys. Rev. B 49, 11919 (1994) ADSCrossRefGoogle Scholar
  3. 3.
    F. Rose, N. Dupuis, Phys. Rev. B 95, 014513 (2017) ADSCrossRefGoogle Scholar
  4. 4.
    M. Lohöfer, T. Coletta, D.G. Joshi, F.F. Assaad, M. Vojta, S. Wessel, F. Mila, Phys. Rev. B 92, 245137 (2015) ADSCrossRefGoogle Scholar
  5. 5.
    F. Rose, F. Léonard, N. Dupuis, Phys. Rev. B 91, 224501 (2015) ADSCrossRefGoogle Scholar
  6. 6.
    Y.T. Katan, D. Podolsky, Phys. Rev. B 91, 075132 (2015) ADSCrossRefGoogle Scholar
  7. 7.
    Y. Nishiyama, Eur. Phys. J. B 89, 31 (2016) ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Rançon, N. Dupuis, Phys. Rev. B 89, 180501 (2014) ADSCrossRefGoogle Scholar
  9. 9.
    M. Stone, P.R. Thomas, Phys. Rev. Lett. 41, 351 (1978) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    M.P.A. Fisher, D.H. Lee, Phys. Rev. B 39, 2756 (1989) ADSCrossRefGoogle Scholar
  11. 11.
    X.G. Wen, A. Zee, Int. J. Mod. Phys. B 04, 437 (1990) ADSCrossRefGoogle Scholar
  12. 12.
    S. Gazit, D. Podolsky, A. Auerbach, Phys. Rev. Lett. 113, 240601 (2014) ADSCrossRefGoogle Scholar
  13. 13.
    J. Corson, R. Mallozz, J. Orenstein, J.N. Eckstein, I. Bozovic, Nature 398, 221 (1999) ADSCrossRefGoogle Scholar
  14. 14.
    R.W. Crane, N.P. Armitage, A. Johansson, G. Sambandamurthy, D. Shahar, G. Grüner, Phys. Rev. B 75, 094506 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    J.F. Sherson, C. Eeitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Nature 467, 68 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    M. Troyer, S. Sachdev, Phys. Rev. Lett. 81, 5418 (1998) ADSCrossRefGoogle Scholar
  17. 17.
    M. Hasenbusch, J. Phys. A 34, 8221 (2001) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, Phys. Rev. E 65, 144520 (2002) CrossRefGoogle Scholar
  19. 19.
    A. Rançson, O. Kdio, N. Dupuis, P. Lecheminant, Phys. Rev. E 88, 012113 (2013) ADSCrossRefGoogle Scholar
  20. 20.
    M. Sentef, M. Kollar, A.P. Kampf, Phys. Rev. B 75, 214403 (2007) ADSCrossRefGoogle Scholar
  21. 21.
    T. Pardini, R.R.P. Singh, A. Katanin, O.P. Sushkov, Phys. Rev. B 78, 024439 (2008) ADSCrossRefGoogle Scholar
  22. 22.
    Y. Kubo, S. Kurihara, J. Phys. Soc. Jpn. 82, 113601 (2013) ADSCrossRefGoogle Scholar
  23. 23.
    Z. Chen, T. Datta, D.-X. Yao, Eur. Phys. J. B 86, 63 (2013) ADSCrossRefGoogle Scholar
  24. 24.
    M.A. Novotny, J. Appl. Phys. 67, 5448 (1990) ADSCrossRefGoogle Scholar
  25. 25.
    A.W. Sandvik, Phys. Rev. B 56, 11678 (1997) ADSCrossRefGoogle Scholar
  26. 26.
    E.R. Gagliano, C.A. Balseiro, Phys. Rev. Lett. 59, 2999 (1987) ADSCrossRefGoogle Scholar
  27. 27.
    P. Nozières, D. Pines, Nuovo Cimento 9 (1958) 470 CrossRefGoogle Scholar
  28. 28.
    D. Pekker, C.M. Varma, Annu. Rev. Condens. Matter Phys. 6, 269 (2015) ADSCrossRefGoogle Scholar
  29. 29.
    J.-P. Blaizot, R. Méndez-Galain, N. Wschebor, Phys. Lett. B 632, 571 (2006) ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    K. Damle, S. Sachdev, Phys. Rev. B 56, 8714 (1997) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsFaculty of Science, Okayama UniversityOkayamaJapan

Personalised recommendations