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

The low-energy constants, namely the staggered magnetization density \hbox{$\tilde{{\cal M}_s}$} 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. \hbox{$\tilde{{\cal M}_s}$} 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 \hbox{$\tilde{{\cal M}_s}$}, 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 \hbox{$\tilde{{\cal M}_s}$} = 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