Onset of ferromagnetism for strongly correlated electrons in one-dimensional chains

TL;DR

This paper investigates the conditions under which Nagaoka ferromagnetism occurs in a one-dimensional infinite-U Hubbard model, revealing that finite closed chains with vacancies exhibit ferromagnetism only for very few electrons, providing insights relevant to recent quantum dot experiments.

Contribution

It provides an exact quantum partition function analysis of Nagaoka ferromagnetism in 1D Hubbard chains, clarifying the conditions for ferromagnetic ground states in finite systems.

Findings

Ground state in open chains is spin-degenerate.

Finite closed chains with vacancies are ferromagnetic only for up to three electrons.

Results support recent experimental observations of Nagaoka ferromagnetism in quantum dots.

Abstract

The existence of the Nagaoka ferromagnetism is examined in the context of the one-dimensional $U=\infty$ Hubbard model. We construct the exact quantum partition function to describe the physics of such a regime. Our calculation reveals that, while the ground state in an open chain is always spin-degenerate, in a finite size closed chain with at least one vacancy, the ground state can only be ferromagnetic when the number of electrons is less or equal to three. Our results shed more light on a very recent experimental verification of Nagaoka ferromagnetism in a quantum dot set up.