Half-filled Hubbard Model on a Bethe lattice with next-nearest neighbor hopping

We study the interplay between N\'eel-antiferromagnetism and the paramagnetic metal-insulator-transition (PMIT) on a Bethe lattice with nearest and next-nearest eighbor hopping $t_1$ and $t_2$. We concentrate in this paper on the situation at half-filling. For $t_2/t_1\to 1$ the PMIT outgrows the antiferromagnetic phase and shows a scenario similar to V$_2$O$_3$. In this parameter regime we also observe a novel magnetic phase.