Ferromagnetism and nonlocal correlations in the Hubbard model

Abstract

We study the possibility and stability of band ferromagnetism in the single-band Hubbard model for the simple cubic (sc) lattice. A nonlocal self-energy is derived within a modified perturbation theory. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of $\mathbf{k}$ dependence. The importance of nonlocal correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase diagram showing regions of ferromagnetic order is calculated for the three-dimensional lattice. Besides, we show results for the optical conductivity and prove that the renormalized one-loop contribution to the conductivity already cancels the Drude peak exactly in case of a local self-energy which is not true anymore for a nonlocal self-energy.