Emergent lattices with geometrical frustration in doped extended Hubbard models

Abstract

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.

Charge orders in organic charge-transfer salts

“…). Furthermore, at t 0 b2 = and t 0 p = (or t 0 q = ) the Hamiltonian reduces to the recently investigated Hubbard model on the honeycomb lattice with anisotropic terms [40].…”

“…Fñ | is a noninteracting fermionic state that is defined as the ground state of an auxiliary Hamiltonian with site-dependent chemical potentials and magnetic order parameters. Such a choice of an auxiliary Hamiltonian allows us to describe both charge and spin orders induced by the intermolecular Coulomb interactions [40,46,47]. In particular, for the insulating states, we consider:…”

“…[35], this two-orbital model reduces to the single-band Hubbard model (at half filling), when the intradimer hopping is very large (i.e., t b1 t b2 , t p , t q ). Furthermore, at t b2 = 0 and t p = 0 (or t q = 0) the Hamiltonian reduces to the recently investigated Hubbard model on the honeycomb lattice with anisotropic terms [40].…”

Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

“…Inclusion of V 1 and/or V 2 gives rise to the competition of magnetic and several CDW states [24][25][26]. In this case, charge and spin degrees of freedom are intertwined, especially, off half filling, and the formation of superstructures often enhances the geometrical frustration of spins that allows noncollinear magnetic order to coexist with the CDW [27].…”

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas

“…Although in the mentioned works the adsorbed particles on surface are rather classical and the analysis of classical lattice gas can give some predictions, taking into account of the quantum properties of adsorbed particles is necessary for, e.g., a description of experiments with He and He [ 28 , 40 , 41 ]. Moreover, there is plethora of recent experimental and theoretical studies of quasi-two-dimensional systems, e.g., Na CoO [ 42 ], NbSe [ 43 , 44 , 45 , 46 , 47 ], TiSe [ 48 ], TaSe [ 49 ], VSe [ 50 ], TaS [ 51 ], and other transition metals dichalcogenides [ 52 ] as well as organic conductors [ 53 , 54 ], where various charge-ordered patterns have been observed on the triangular lattice. However, for such phenomena the atomic limit of the model studies is less reliable and more realistic description includes also electron hoping term as in the extended Hubbard model [ 15 , 16 , 17 , 18 , 19 ] or coupling with phonons as in the Holstein-Hubbard model [ 55 ].…”