Itinerant ferromagnetism from one-dimensional mobility

I will present a universal kinetic mechanism for half-metallic ferromagnetism, a metallic state with full spin polarization, arising from strong on-site Coulomb repulsions and constrained one-dimensional (1D) dynamics of particles. I will begin by illustrating this mechanism through a solvable model on a Lieb lattice, where doped electrons exhibit 1D mobility. This 1D motion leads exclusively to multi-spin ring exchanges of even parity, which drive ferromagnetism and stabilize a unique half-metallic ground state. Unlike the Nagaoka mechanism, this result holds for any doped electron density in the thermodynamic limit. I will also discuss microscopic realizations of this mechanism, focusing on two examples: doped holes in the strong-coupling regime of the Emery model and vacancies in a two-dimensional Wigner crystal. Finally, I will highlight an intriguing exact equivalence between the bosonic and fermionic versions of these models, which suggests a novel mechanism for the conjectured Bose metallic phase.