On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet

TL;DR

This paper investigates the ferromagnetic susceptibility in the SU(N) Hubbard Model at low hole density, revealing an exponential divergence at low temperatures and showing how ferromagnetism diminishes with increasing N.

Contribution

It provides a detailed analysis of the divergence of ferromagnetic susceptibility in the SU(N) Hubbard Model, demonstrating the existence of the Nagaoka-Thouless ferromagnetic state at low densities and temperatures, and how it scales with N.

Findings

Ferromagnetic susceptibility diverges exponentially as temperature approaches zero.

The ferromagnetic state exists at low hole density and low temperature.

The characteristic temperature scale decreases with increasing N.

Abstract

Using finite temperature strong coupling expansions for the SU(N) Hubbard Model, we calculate the thermodynamic properties of the model in the infinite-$U$ limit for arbitrary density $0\leq \rho \leq 1$ and all $N$. We express the ferromagnetic susceptibility of the model as a Curie term plus a $\Delta \chi$, an excess susceptibility above the Curie-behavior. We show that, on a bipartite lattice, graph by graph the contributions to $\Delta \chi$ are non-negative in the limit that the hole density $\delta=1-\rho$ goes to zero. By summing the contributions from all graphs consisting of closed loops we find that the low hole-density ferromagnetic susceptibility diverges exponentially as $\exp{\Delta /T}$ as $T \to 0$ in two and higher dimensions. This demonstrates that Nagaoka-Thouless ferromagnetic state exists as a thermodynamic state of matter at low enough density of holes and sufficiently low temperatures. The constant $\Delta$ scales with the SU(N) parameter $N$ as $1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as the characteristic temperature scale for ferromagnetic order goes down.