The (extended) Hubbard model on the triangular lattice: how correlation and frustration lead to competing spin-liquid, magnetic-order and charge-order phases In the first part of the talk, we study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters in different spatial directions, and is relevant for layered organic charge-transfer salts and for the inorganic compounds Cs2CuBr4 and Cs2CuCl4.[1,2] By using variational wave functions which include both Jastrow and backflow terms, we provide solid evidence that two spin-liquid phases are stabilized in the strongly correlated regime, while states with spiral magnetic order and a non trivial pitch vector are found close to the isotropic point. Two different kinds of collinear orders are found in a wide region of the phase diagram close, respectively, to the limits of square lattice and decoupled one-dimensional chains. We also introduce another family of organic charge-transfer salts where a fully anisotropic triangular-lattice description produces importantly different results, including a significant lowering of the critical U of the spin-liquid phase.[3]

In the second part of the talk, we consider the extended Hubbard model on the isotropic triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions leads to exotic phases where charge order, antiferromagnetic order, and metallic conductivity can coexist. Our variational Monte Carlo simulations show that three kinds of ordered metallic states are stable as a function of nearest-neighbor interaction and filling. In one of the phases, the coexistence of conductivity and order is explained by a separation into two functional classes of particles: part of them contributes to the stable order, while the other part forms a partially filled band on the remaining substructure.[4]

[1] Tocchio, Feldner, Becca, Valenti, Gros, PRB 87, 035143 (2013)
[2] Tocchio, Gros, Valenti, Becca, PRB 89, 235107 (2014)
[3] Jacko, Tocchio, Jeschke, Valenti, PRB 88, 155139 (2013)
[4] Tocchio, Gros, Zhang, Eggert, arXiv:1402.3160