Effect of Ring Exchange on Orbital Antiferromagnet

We study the effect of four-particle ring exchange process on orbital antiferromagnetic state that occurs in some correlated electron systems in two dimensions. The primary question is whether the ring exchange process enhances or suppresses the orbital antiferromagnetic ordering. Using the fact that the orbital antiferromagnetic state arises in the large-N limit of the SU(N) generalization of the t-J model, we consider the large-N limit of the t-J-$K$ model where $K$ represents the four-particle ring exchange term. The phase diagrams in the large-N mean field theory are obtained for the half-filling and finite hole concentrations at zero temperature. It is found that the ring exchange in general favors dimerized states or the inhomogeneous orbital antiferromagnetic state, and suppresses the homogeneous orbital antiferromagnetic state. We compare our results with other related models of strongly correlated systems with ring exchange processes.