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.
Similar content being viewed by others
References
S. Gazit, D. Podolsky, A. Auerbach, D.P. Arovas, Phys. Rev. B 88, 235108 (2013)
A.V. Chubukov, S. Sachdev, J. Ye, Phys. Rev. B 49, 11919 (1994)
F. Rose, N. Dupuis, Phys. Rev. B 95, 014513 (2017)
M. Lohöfer, T. Coletta, D.G. Joshi, F.F. Assaad, M. Vojta, S. Wessel, F. Mila, Phys. Rev. B 92, 245137 (2015)
F. Rose, F. Léonard, N. Dupuis, Phys. Rev. B 91, 224501 (2015)
Y.T. Katan, D. Podolsky, Phys. Rev. B 91, 075132 (2015)
Y. Nishiyama, Eur. Phys. J. B 89, 31 (2016)
A. Rançon, N. Dupuis, Phys. Rev. B 89, 180501 (2014)
M. Stone, P.R. Thomas, Phys. Rev. Lett. 41, 351 (1978)
M.P.A. Fisher, D.H. Lee, Phys. Rev. B 39, 2756 (1989)
X.G. Wen, A. Zee, Int. J. Mod. Phys. B 04, 437 (1990)
S. Gazit, D. Podolsky, A. Auerbach, Phys. Rev. Lett. 113, 240601 (2014)
J. Corson, R. Mallozz, J. Orenstein, J.N. Eckstein, I. Bozovic, Nature 398, 221 (1999)
R.W. Crane, N.P. Armitage, A. Johansson, G. Sambandamurthy, D. Shahar, G. Grüner, Phys. Rev. B 75, 094506 (2007)
J.F. Sherson, C. Eeitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Nature 467, 68 (2010)
M. Troyer, S. Sachdev, Phys. Rev. Lett. 81, 5418 (1998)
M. Hasenbusch, J. Phys. A 34, 8221 (2001)
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, Phys. Rev. E 65, 144520 (2002)
A. Rançson, O. Kdio, N. Dupuis, P. Lecheminant, Phys. Rev. E 88, 012113 (2013)
M. Sentef, M. Kollar, A.P. Kampf, Phys. Rev. B 75, 214403 (2007)
T. Pardini, R.R.P. Singh, A. Katanin, O.P. Sushkov, Phys. Rev. B 78, 024439 (2008)
Y. Kubo, S. Kurihara, J. Phys. Soc. Jpn. 82, 113601 (2013)
Z. Chen, T. Datta, D.-X. Yao, Eur. Phys. J. B 86, 63 (2013)
M.A. Novotny, J. Appl. Phys. 67, 5448 (1990)
A.W. Sandvik, Phys. Rev. B 56, 11678 (1997)
E.R. Gagliano, C.A. Balseiro, Phys. Rev. Lett. 59, 2999 (1987)
P. Nozières, D. Pines, Nuovo Cimento 9 (1958) 470
D. Pekker, C.M. Varma, Annu. Rev. Condens. Matter Phys. 6, 269 (2015)
J.-P. Blaizot, R. Méndez-Galain, N. Wschebor, Phys. Lett. B 632, 571 (2006)
K. Damle, S. Sachdev, Phys. Rev. B 56, 8714 (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nishiyama, Y. Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model. Eur. Phys. J. B 91, 69 (2018). https://doi.org/10.1140/epjb/e2018-80707-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2018-80707-7