High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

作者：Jiang F J^*

来源：European Physical Journal B, 2012, 85(12): 402.

DOI：10.1140/epjb/e2012-30784-7

The low-energy constants, namely the staggered magnetization density (M) over tilde (s) per spin, the spin stiffness rho(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. (M) over tilde (s) and rho(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 (M) over tilde (s), rho(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 (M) over tilde (s) = 0.26882(3), rho(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.

• 出版日期2012-12