Mott transition in the two-dimensional Hubbard model

We are interested in the description of the Mott-Hubbard transition from a perturbation theory arising from a two-dimensional Hubbard model. We calculate the self-energy within the random phase approximation and a double-Lorentzian as a non-interacting density of states. The paramagnetic ground state is unstable for realistic values of U, since the self-energy presents some inconsistencies; one of them is that its imaginary part presents more than one zero, which is a violation of the Luttinger theorem. We use a Bogolyubov transformation and within a spin density wave mean field, the antiferromagnetic correlations of wave vector Q = (π/a,π/a) are included. We recalculate the self-energy in the new ground state and then it is able to describe the Mott-Hubbard transition, and the Luttinger theorem is satisfied.