Dynamical mean field theory equations on nearly real frequency axis

The iterated perturbation theory (IPT) equations of the dynamical mean field theory (DMFT) for the half-filled Hubbard model are solved on nearly real frequencies at various values of the Hubbard parameters, U, to investigate the nature of metal-insulator transition (MIT) at finite temperatures. This method avoids the instabilities associated with the infamous Padé analytic continuation and reveals fine structures across the MIT at finite temperatures, which cannot be captured by conventional methods for solving DMFT-IPT equations on Matsubara frequencies. Our method suggests that at finite temperatures, there is a crossover from a bad metal to a bad insulator in which the height of the quasi-particle (Kondo) peak decreases to a non-zero small bump, which gradually suppresses as one moves deeper into the bad insulating regime.