Variational RVB Wave Function for the Spin-1/2 Heisenberg Model on Honeycomb Lattice

In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground-state of the S = 1/2 antiferromagnetic Heisenberg model on the honeycomb lattice. Employing the variational Monte Carlo (VMC) method, we show that the ground-state energy obtained from such a resonating valence bond (RVB) wave function, lies well below the energy of the Neel state and compares very well to the energies evaluated on the basis of the spin-wave theory and by the series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are different, which indicates the anisotropic nature of the system. We compare our results with that of the square lattice, and we show that although the quantum fluctuations on the honeycomb lattice are much stronger, they do not destroy the magnetic order completely.