Emergent lattices with geometrical frustration in doped extended Hubbard models

Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site U and nearest-neighbor V Coulomb interactions at 3/4 filling (n=3/2) and (ii) the triangular lattice with on-site U, nearest-neighbor V, and next-nearest-neighbor V' Coulomb interactions at 3/8 filling (n=3/4). We consider various approaches including mean-field approximations, perturbation theory, and variational Monte Carlo. For the honeycomb case (i), charge order induces an effective triangular lattice at large values of U/t and V/t, where t is the nearest-neighbor hopping integral. The nearest-neighbor spin exchange interactions on this effective triangular lattice are antiferromagnetic in most of the phase diagram, while they become ferromagnetic when U is much larger than V. At U/t∼(V/t)^3, ferromagnetic and antiferromagnetic exchange interactions nearly cancel out, leading to a system with four-spin ring-exchange interactions. On the other hand, for the triangular case (ii) at large U and finite V', we find no charge order for small V, an effective kagome lattice for intermediate V, and one-dimensional charge order for large V. These results indicate that Coulomb interactions induce [case (i)] or enhance [case(ii)] emergent geometrical frustration of the spin degrees of freedom in the system, by forming charge order.