Lattice dependence of saturated ferromagnetism in the Hubbard model

TL;DR

This paper studies the conditions under which saturated ferromagnetism occurs in the Hubbard model across different lattices, emphasizing the role of density of states features in stabilizing Nagaoka ferromagnetism.

Contribution

It develops a variational resolvent method to analyze Nagaoka instability for all U values, improving bounds on ferromagnetic regimes in the Hubbard model.

Findings

Particle-hole asymmetry promotes ferromagnetism.

Diverging density of states at the band edge stabilizes Nagaoka ferromagnetism.

Results apply to various lattices in 2D and 3D.

Abstract

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and d=3. A variational resolvent approach is developed for the Nagaoka instability both for U = infinity and for U < infinity which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low density limit.