Absence of Spin Liquid in Nonfrustrated Correlated Systems

The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (also known as graphene) lattice is revisited. The variational cluster approximation, the cluster dynamical mean field theory, and the cluster dynamical impurity approximation are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase in this nonfrustrated system, we find that the Mott transition is preempted by a magnetic transition occurring at a lower value of the interaction U, and therefore the spin liquid phase does not occur. This conclusion is obtained using clusters with two bath orbitals connected to each boundary cluster site. We argue that using a single bath orbital per boundary site is insufficient and leads to the erroneous conclusion that the system is gapped for all nonzero values of U.