Emergent lattices with geometrical frustration in doped extended Hubbard models

TL;DR

This paper explores how charge ordering in doped extended Hubbard models on honeycomb and triangular lattices leads to emergent lattice structures with geometrical frustration, revealing new magnetic interactions and phases.

Contribution

It demonstrates that Coulomb interactions induce or enhance geometrical frustration through charge order, resulting in emergent lattices like triangular and kagome structures.

Findings

Charge order induces an effective triangular lattice in honeycomb models.

Antiferromagnetic and ferromagnetic exchange interactions depend on interaction ratios.

Emergent lattices like kagome and one-dimensional charge order appear in triangular 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 $U/t\sim (V/t)^3$, 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.