Frustration induced Itinerant Ferromagnetism of Fermions in Optical Lattice

When the Fermi Hubbard model was first introduced sixty years ago, one of the original motivations was to understand correlation effects in itinerant ferromagnetism. In the past two decades, ultracold Fermi gas in an optical lattice has been used to study the Fermi Hubbard model. However, the metallic ferromagnetic correlation was observed only in a recent experiment using frustrated lattices, and its underlying mechanism is not clear yet. In this letter, we point out that, under the particle--hole transformation, the single-particle ground state can exhibit double degeneracy in such a frustrated lattice. Therefore, the low-energy state exhibits valley degeneracy, reminiscent of multi-orbit physics in ferromagnetic transition metals. The local repulsive interaction leads to the valley Hund's rule, responsible for the observed ferromagnetism. We generalize this mechanism to distorted honeycomb lattices and square lattices with flux. This mechanism was first discussed by M\"uller-Hartmann in a simpler one-dimension model. However, this mechanism has not been widely discussed and has not been related to experimental observations before. Hence, our study not only explains the experimental findings but also enriches our understanding of itinerant ferromagnetism.