"Linearized" dynamical mean-field theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling bet ween the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are lineari zed, and the value for the critical Coulomb repulsion Uc can be calculated analytically. For the symmetric single-band Hubbard model at zero temperatu re, the critical value is found to be given by 6 times the square root of t he second moment of the free (U = 0) density of states. This result is in g ood agree ment with the numerical value obtained from the Projective Selfco nsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generaliz ation to more complicated lattices is discussed. The "linearized DMFT" yiel ds plausible results for the complete geometry dependence of the critical i nteraction.