We present spectral and optical properties of the Hubbard model on a two-dimensional square lattice using a generalization of dynamical mean-field theory to magnetic states in a finite dimension. The self-energy includes the effect of spin fluctuations and screening of the Coulomb interaction due to particle-particle scattering. At half-filling the quasiparticles reduce the width of the Mott-Hubbard "gap" and have dispersions and spectral weights that agree remarkably well with quantum Monte Carlo and exact diagonalization calculations. Away from half-filling we consider incommensurate magnetic order with a varying local spin direction, and derive the photoemission and optical spectra. The incommensurate magnetic order leads to a pseudogap which opens at the Fermi energy and coexists with a large Mott-Hubbard gap. The quasiparticle states survive in the doped systems, but their dispersion is modified by the doping, and a rigid-band picture does not apply. Spectral weight in the optical conductivity is transferred to lower energies, and the Drude weight increases linearly with increasing doping. We show that incommensurate magnetic order also leads to midgap states in the optical spectra and to decreased scattering rates in the transport processes, in qualitative agreement with the experimental observations in doped systems. The gradual disappearence of the spiral magnetic order and the vanishing pseudogap with increasing temperature is found to be responsible for the linear resistivity. We discuss the possible reasons why these results may only partially explain the features observed in the optical spectra of high-temperature superconductors.
 

Physical Review B, 60 5224-43, 1999.