Analytic properties of insulating solution of half-filled Hubbard model

We discuss analytic properties of insulating solution of half-filled Hubbard model on the hypercubic lattice within DMFT framework. We use an approximation where Green’s function is obtained as an average of two magnetic Hartree-Fock solutions. Under that assumption we obtain relations for the Green’s function, self-energy and quasi-particle scattering time in two limiting cases, around zero frequency and at large frequencies, and a critical value of interaction $U_c$ leading to metal-insulator transition. We compare our results for $U_c$ with other approaches, including numerical renormalization group and iterated perturbation theory (IPT). We also discuss a possibility of extending our method to IPT approximation, which is widely used in studying half-filled Hubbard model in infinite dimensions.