The Hubbard model on the triangular lattice: Spiral order and spin liquid

TL;DR

This study uses the variational cluster approximation to explore the phase diagram of the half-filled Hubbard model on a triangular lattice, revealing transitions from spiral magnetic order to a spin liquid and then to a metal as interaction strength varies.

Contribution

It provides a detailed phase diagram of the Hubbard model on a triangular lattice, identifying the conditions for spiral order, spin liquid, and metallic phases using cluster calculations.

Findings

Transition from spiral order to spin liquid as U decreases.

Identification of a metallic phase for U less than approximately 6.7t.

Extrapolation suggests a disordered phase at U=8t and spiral order at U greater than approximately 12t.

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 non-magnetic Mott insulating phase -- a spin liquid -- and then, for $U\lesssim6.7t$, 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 $U\gtrsim 12$.