Proposal of an extendedt−JHamiltonian for high-Tccuprates fromab initiocalculations on embedded clusters

A series of accurate ab initio calculations on ${\mathrm{Cu}}_p{\mathrm{O}}_q$ finite clusters, properly embedded in the Madelung potential of the infinite lattice, have been performed in order to determine the local effective interactions in the ${\mathrm{CuO}}_2$ planes of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ compounds. The values of the first-neighbor interactions, magnetic coupling ${(J}_{\mathrm{NN}}=125\mathrm{}$ meV), and hopping integral ${(t}_{\mathrm{NN}}=-555$ meV) have been confirmed. Important additional effects are evidenced, concerning essentially the second-neighbor hopping integral $t_{\mathrm{NNN}}=+110\mathrm{}$ meV, the displacement of a singlet toward an adjacent colinear hole, $h_{\mathrm{SD}}^{\mathrm{abc}}=-80$ meV, a non-negligible hole-hole repulsion $V_{\mathrm{NN}}-V_{\mathrm{NNN}}=0.8\mathrm{}$ eV, and a strong anisotropic effect of the presence of an adjacent hole on the values of the first-neighbor interactions. The dependence of $J_{\mathrm{NN}}$ and $t_{\mathrm{NN}}$ on the position of neighbor hole(s) has been rationalized from the two-band model and checked from a series of additional ab initio calculations. An extended $t-J$ model Hamiltonian has been proposed on the basis of these results. It is argued that the here-proposed three-body effects may play a role in the charge/spin separation observed in these compounds, that is, in the formation and dynamic of stripes.