Scaling properties of the ferromagnetic state in the Hubbard model

TL;DR

This paper uses numerical scaling to analyze the transition from ferromagnetic to antiferromagnetic states in the 2D Hubbard model, revealing a discontinuous change in total spin as interaction strength varies.

Contribution

It demonstrates that Nagaoka's ferromagnetic state is replaced by an antiferromagnetic state with a spin jump at finite Hubbard U, highlighting a crossover in the thermodynamic limit.

Findings

Nagaoka's ferromagnetic state is superseded by an AF state at finite U.

Discontinuous jump in total spin occurs during the transition.

Crossover indicates a precursor to state coalescence at infinite U.

Abstract

A numerical scaling analysis is used to show that Nagaoka's ferromagnetic state in two-dimensional Hubbard model with one hole is supersede by an antiferromagnetic (AF) state with a discontinuous jump in the total spin due to the AF coupling as the Hubbard $U$ is made finite. The same applies to the two-hole system, which has a spiral spin structure. We can show, via the scaling, that the crossover to an AF state is a precursor of a pathological coalescence of states having the minimum spin and Nagaoka's state at $U=\infty$ in the thermodynamic limit.