Spin liquid ground state on the honeycomb Heisenberg spin 1/2 model with nearest and next nearest neighbor interaction

We numerically investigate the S=1/2 Heisenberg model on the honeycomb lattice with nearest ($J_1$) and next-nearest neighbor ($J_2$) interactions with the density matrix renormalization group (DMRG). We are able to study open cylinders with widths up to 12 lattice spacings. For $J_2/J_1$ near $0.3$, we find a spin liquid phase, bordered by an antiferromagnetic phase for smaller $J_2$ and a valence bond crystal for larger $J_2$. For the spin liquid phase we find finite spin singlet and triplet gaps and short spin-spin and bond-bond correlation lengths. We also find that the energy splitting between the two different topological sectors decays exponentially with the system width, consistent with a gapped Z2 spin liquid.