Circulating-current states and ring-exchange interactions in cuprates

We consider the consequences for circulating-current states of a cyclic, four-spin, "ring-exchange" interaction of the type shown recently to be significant in cuprate systems. The real-space Hartree-Fock approach is used to establish the existence of charge-current and spin-current phases in a generalized Hubbard model for the CuO2 planes in cuprates. We augment the Hartree-Fock approximation to consider correlated states renormalized by Gutzwiller projection factors, which allow us to gauge the qualitative effects of projection to no double occupancy in the limit of strong on-site Coulomb repulsion. We find that charge flux states may be competitive in the underdoped and optimally doped regime in cuprate systems, whereas spin flux states are suppressed in the strongly correlated regime. We then include the ring-exchange interaction and demonstrate its effect on current-carrying states both at and away from half-filling.