Stable and Metastable Kinetic Ferromagnetism on a Ring

Abstract

Performing an exact diagonalization of the effective spin problem, a ferromagnetic ground state of kinetic origin is shown to emerge in a system of $N$ strongly correlated electrons on a $L$-site ring ($L>N$). This phenomenon is brought about by the quantum necklace statistics originated from the no double occupancy constraint leading to a fractional shifted electron momentum quantization. As a consequence of such special energy level distribution, the kinetic ferromagnetism is stable only for $N=3$. For odd $N>3$ the fully polarized FM state energy is only a local minimum but it is protected by a finite energy barrier that inhibits one spin-flip processes. The metastable ferromagnetic state survives perturbations of small magnitude opening up a possibility of being experimentally observed by an appropriate tuning of the interdot tunneling amplitudes in currently available quantum dot arrays.