Metal-insulator transition and magnetic ordering in Hubbard models near the Nagaoka limit

We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. The analysis simplifies near the ferromagnetic limit. We find that the two dimensional(2D) Hubbard model has a charge excitation gap at half-filling for any finite U in this region on both the bipartite square lattice and the nonbipartite triangular lattice. In some cases, the system goes through a first-order phase transition to become a paramagnetic metal as $S_{z}$ is lowered. We also discuss the extension to the doped case. We find that in the large U limit, a single doped hole has a bandwidth of order of J rather than t at $S_{z}=0$.