  Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a
spin liquid phase (SL) that intervenes between the antiferromagnetic and
semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To
better understand the nature of this exotic phase, we study the quantum
$J_1-J_2$ spin model on the honeycomb lattice, which provides an effective
description of the Mott insulating region of the Hubbard model. Employing the
variational Monte Carlo approach, we analyze the phase diagram of the model,
finding a phase transition between antiferromagnet and an unusual $Z_2$ SL
state at $J_2/J_1\approx 0.08$, which we identify as the SL phase of the
Hubbard model. At higher $J_2/J_1\gtrsim 0.3$ we find a transition to a
dimerized state with spontaneously broken rotational symmetry.
