  We use density matrix renormalization group (DMRG) algorithm to study the
phase diagram of the spin-1/2 Heisenberg model on honeycomb lattice with first
(J1) and second (J2) neighbor antiferromagnetic interactions, where a Z2 spin
liquid region has been proposed. By implementing SU(2) symmetry in the DMRG
code, we are able to obtain accurate results for long cylinders with width
slightly over 15 lattice spacings and torus up to the size N=2*6*6. With
increasing J2, we find a Neel phase with vanishing spin gap and a plaquette
valence-bond (PVB) phase with non-zero spin gap. By extrapolating the square of
the staggered magnetic moment ms^2 on finite-size cylinders to thermodynamic
limit, we find the Neel order vanishing at J2/J1~0.22. For 0.25<J2/J1<0.35, we
find a possible PVB order, which shows a fast growing PVB decay length with
increasing system width. For 0.22<J2/J1<0.25, both spin and dimer orders are
weak for all systems we have studied, which is consistent with a possible spin
liquid phase or a deconfined quantum critical point. We present calculations of
the topological entanglement entropy, compare the DMRG results with the
variational Monte Carlo, and discuss possible scenarios in the thermodynamic
limit for this region.
