Calculation of the four-spin cyclic exchange in cuprates

Abstract

Starting from the three-band Hubbard model for the cuprates, we calculate analytically the four-spin cyclic exchange in the limit of infinite on-site Coulomb repulsion and zero O-O hopping tpp using two methods: (i) perturbation theory in tpd/Δ, where tpd is the Cu-O hopping and Δ the Cu-O charge transfer energy and (ii) exact solution of a Cu4O4 plaquette. The latter method coincides with the first to order eight in tpd and permits us to extend the results to tpd/Δ of order one. The results are relevant to recent experimental and theoretical research that relate the splitting of certain spin excitations with Δ and the superconducting critical temperature.