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

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 than or equal to three. Our results shed more light on a very recent experimental verification of Nagaoka ferromagnetism in a quantum dot setup.

Figure 1

Energy gap between the FM ground state and the first unpolarized excited state. For $L=N=3$, all spin states are degenerate and have energy equal to zero.

Figure 2

Necklaces that can be formed with $N=4$ projected electrons. Each color represents one of the two spin polarization states.