https://doi.org/10.1140/epjb/e2012-30784-7
Regular Article
High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice
Department of Physics, National Taiwan Normal
University, 88, Sec. 4, Ting-Chou
Rd., 116 Taipei, Taiwan, China
a e-mail: fjjiang@ntnu.edu.tw
Received:
28
August
2012
Received in final form:
3
October
2012
Published online:
6
December
2012
The low-energy constants, namely the staggered magnetization density 
per spin, the spin stiffness
ρs, 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. and ρs 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 , ρs, 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 = 0.26882(3),
ρs = 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.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012
