Hubbard Model on the Triangular Lattice: Spiral Order and Spin Liquid

Abstract

We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion $U$ (or equivalently increasing pressure) we go from a phase with long-range, three-sublattice, spiral magnetic order, to a nonmagnetic Mott insulating phase—a spin liquid—and then, for $U\lesssim 6.7t$, to a metallic phase. Clusters of sizes 3, 6, and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at $U=8t$, but to a spiral order at $U\gtrsim 12$.