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 Δ. 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.