Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

TL;DR

This paper refines the criteria for the stability of ferromagnetism in the Hubbard model on a square lattice, providing more accurate critical parameters for the Nagaoka state using advanced variational wave functions.

Contribution

It introduces an improved instability criterion for the Nagaoka ferromagnetic state in the Hubbard model, incorporating correlation effects near a spin flip.

Findings

Critical hole density δ_cr = 0.251 at U = ∞

Critical coupling U_cr = 77.7 t

Significant improvement over previous variational results

Abstract

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of $\delta_{cr} = 0.251$ for $U = \infty$ and a critical coupling of $U_{cr} = 77.7 t$. Both values improve previous variational results considerably.