Metal-Insulator Transition in the Presence of Van Hove Singularities for Bipartite Lattices

We have considered the phase diagram of the ground state for the t-t' Hubbard model with half-filling of the band. The criterion for the metal-insulator transition has been formulated using the analytic expansion in transfer integral t' and in direct antiferromagnetic gap Delta. For a square lattice, there exists an interval of t' values for which the metal-insulator transition is of the first order due to the existence of the Van Hove singularity. For simple and body-centered cubic lattices, a transition occurring from the insulator antiferromagnetic state to the antiferromagnetic metal phase is a second-order transition followed by a transition to paramagnetic metal.