Nature of the spin liquid state of the Hubbard model on a honeycomb lattice

Recent numerical work indicates the existence of a spin liquid (SL) phase 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. We find three phases-antiferromagnetic, an unusual Z ₂ SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z ₂ SL state as the likely candidate for the SL phase of the Hubbard model.