Spiral Magnets as Gapless Mott Insulators

TL;DR

This paper demonstrates that in the large U limit of the Hubbard model on a triangular lattice, the interplay of spin and charge excitations results in a gapless insulating state with finite-frequency conductivity, contrasting with square-lattice behavior.

Contribution

It reveals that non-collinear spin order causes coupled spin-charge modes, leading to gapless Mott insulators with finite-frequency conductivity, a novel insight into strongly correlated systems.

Findings

Goldstone modes are a mixture of spin and charge beyond leading order in t/U.

The system exhibits non-vanishing conductivity at finite frequencies.

The magnet remains insulating at zero frequency.

Abstract

In the large $U$ limit, the ground state of the half-filled, nearest-neighbor Hubbard model on the triangular lattice is the three-sublattice antiferromagnet. In sharp contrast with the square-lattice case, where transverse spin-waves and charge excitations remain decoupled to all orders in $t/U$, it is shown that beyond leading order in $t/U$ the three Goldstone modes on the triangular lattice are a linear combination of spin and charge. This leads to non-vanishing conductivity at any finite frequency, even though the magnet remains insulating at zero frequency. More generally, non-collinear spin order should lead to such gapless insulating behavior.