Abstract
The low-energy constants, namely the staggered magnetization density M̃ s per spin, the spin stiffness ρ s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M̃ s and ρ s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M̃ s , ρ s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M̃ s = 0.26882(3), ρ s = 0.1012(2)J, and c = 1.2905(8)Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.
Similar content being viewed by others
References
J. Gasser, H. Leutwyler, Ann. Phys. 158, 142 (1984)
J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)
S. Chakravarty, B.I. Halperin, D.R. Nelson, Phys. Rev. B 39, 2344 (1989)
H. Neuberger, T. Ziman, Phys. Rev. B 39, 2608 (1989)
P. Hasenfratz, H. Leutwyler, Nucl. Phys. B 343, 241 (1990)
F.-J. Jiang, U.-J. Wiese, Phys. Rev. B 83, 155120 (2011)
A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)
M. Creutz, J. High Energy Phys. 04, 017 (2008)
A. Borii, Phys. Rev. D 78, 074504 (2008)
P.F. Bedaque, M.I. Buchoff, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 78, 017502 (2008)
S. Okubo et al., J. Phys. Soc. Jpn 80, 023705 (2011)
F.-J. Jiang, F. Kampfer, M. Nyfeler, U.-J. Wiese, Phys. Rev. B 78, 214406 (2008)
U.-J. Wiese, H.-P. Ying, Z. Phys. B 93, 147 (1994)
A.W. Sandvik, Phys. Rev. B 56, 18 (1997)
F.-J. Jiang, F. Kämpfer, M. Nyfeler, Phys. Rev. B 80, 033104 (2009)
S. Wenzel, W. Janke, A.M. Läuchli, Phys. Rev. E 81, 066702 (2010)
P. Hasenfratz, F. Niedermayer, Z. Phys. B 92, 91 (1993)
B.B. Beard, U.-J. Wiese, Phys. Rev. Lett. 77, 5130 (1996)
A.F. Albuquerque et al., J. Magn. Magn. Mater. 310, 1187 (2007)
B. Bauer et al., J. Stat. Mech. P05001 (2011)
F.-J. Jiang, Phys. Rev. B 83, 024419 (2011)
A. Mattsson, P. Fröjdh, T. Einarsson, Phys. Rev. B 49, 3997 (1994)
E.V. Castro, N.M.R. Peres, K.S.D. Beach, A.W. Sandvik, Phys. Rev B 73, 054422 (2006)
Z. Weihong, J. Oitmaa, C.J. Hamer, Phys. Rev. B 44, 11869 (1991)
J. Oitmaa, C.J. Hamer, Z. Weihong, Phys. Rev. B 45, 9834 (1992)
S. Wenzel, A.M. Läuchli, Phys. Rev. Lett. 106, 197201 (2011)
S. Wenzel, A.M. Läuchli, J. Stat. Mech. P09010 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, F. High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice. Eur. Phys. J. B 85, 402 (2012). https://doi.org/10.1140/epjb/e2012-30784-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-30784-7