Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular, honeycomb and kagome lattices

TL;DR

This study investigates the stability of Nagaoka ferromagnetism in the two-dimensional Hubbard model across different lattices, revealing lattice-dependent stability thresholds and extending understanding of ferromagnetic phases.

Contribution

It provides a detailed analysis of the lattice dependence of Nagaoka ferromagnetism, including improved critical density estimates and stability regions on triangular, kagome, and honeycomb lattices.

Findings

Nagaoka ferromagnetism is stable on non-bipartite lattices for certain fillings.

The critical density for instability on the triangular lattice is 1.887 at U=∞.

Ferromagnetic stability regions are larger than previously estimated, especially on kagome lattices.

Abstract

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarized ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of $n=1.887$ at $U=\infty$, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.